SUPPORT THE WORK

# GetWiki

### general relativity

ARTICLE SUBJECTS
news  →
unix  →
wiki  →
ARTICLE TYPES
feed  →
help  →
wiki  →
ARTICLE ORIGINS
general relativity
[ temporary import ]
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{For|the graduate textbook by Robert Wald|General Relativity (book)}}{{short description|Einstein's theory of gravitation as curved spacetime}}{{see introduction}}
{{General relativity sidebar}}File:BBH gravitational lensing of gw150914.webm|266px |thumb|Slow motion computer simulation of the black hole binary system GW150914 as seen by a nearby observer, during 0.33 s of its final inspiral, merge, and ringdown. The star field behind the black holes is being heavily distorted and appears to rotate and move, due to extreme gravitational lensing, as spacetime itself is distorted and dragged around by the rotating (black hole]]s.WEB,weblink GW150914: LIGO Detects Gravitational Waves, Black-holes.org, 18 April 2016, )General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the {{vanchor|curvature of spacetime|Spacetime curvature|curvature of spacetime}} is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay. The predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.Einstein's theory has important astrophysical implications. For example, it implies the existence of black holesâ€”regions of space in which space and time are distorted in such a way that nothing, not even light, can escapeâ€”as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes. For example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes, respectively. The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.Widely acknowledged as a theory of extraordinary beauty, general relativity has often been described as the most beautiful of all existing physical theories.{{TOC limit|limit=3}}

## History

Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations.O'Connor, J.J. and Robertson, E.F. (1996), General relativity. Mathematical Physics index, School of Mathematics and Statistics, University of St. Andrews, Scotland. Retrieved 2015-02-04. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, and form the core of Einstein's general theory of relativity.{{Harvnb|Pais|1982|loc=ch. 9 to 15}}, {{Harvnb|Janssen|2005}}; an up-to-date collection of current research, including reprints of many of the original articles, is {{Harvnb|Renn|2007}}; an accessible overview can be found in {{Harvnb|Renn|2005|pp=110ff}}. Einstein's original papers are found in Digital Einstein, volumes 4 and 6. An early key article is {{Harvnb|Einstein|1907}}, cf. {{Harvnb|Pais|1982|loc=ch. 9}}. The publication featuring the field equations is {{Harvnb|Einstein|1915}}, cf. {{Harvnb|Pais|1982|loc=ch. 11â€“15}} The 19th century mathematician Bernhard Riemann's non-Euclidean geometry, called Riemannian Geometry, provided the key mathematical framework which Einstein fit his physical ideas of gravity on, and enabled him to develop general relativity.Moshe Carmeli (2008).Relativity: Modern Large-Scale Structures of the Cosmos. pp.92, 93.World Scientific PublishingThe Einstein field equations are nonlinear and very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, which eventually resulted in the Reissnerâ€“NordstrÃ¶m solution, now associated with electrically charged black holes.{{Harvnb|Schwarzschild|1916a}}, {{Harvnb|Schwarzschild|1916b}} and {{Harvnb|Reissner|1916}} (later complemented in {{Harvnb|NordstrÃ¶m|1918}}) In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equationsâ€”the cosmological constantâ€”to match that observational presumption.{{Harvnb|Einstein|1917}}, cf. {{Harvnb|Pais|1982|loc=ch. 15e}} By 1929, however, the work of Hubble and others had shown that our universe is expanding. This is readily described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant. LemaÃ®tre used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an extremely hot and dense earlier state.Hubble's original article is {{Harvnb|Hubble|1929}}; an accessible overview is given in {{Harvnb|Singh|2004|loc=ch. 2â€“4}} Einstein later declared the cosmological constant the biggest blunder of his life.As reported in {{Harvnb|Gamow|1970}}. Einstein's condemnation would prove to be premature, cf. the section Cosmology, belowDuring that period, general relativity remained something of a curiosity among physical theories. It was clearly superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters ("(wikt:fudge factor|fudge factors)").{{Harvnb|Pais|1982|pp=253â€“254}} Similarly, a 1919 expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, 1919,{{Harvnb|Kennefick|2005}}, {{Harvnb|Kennefick|2007}} making Einstein instantly famous.{{Harvnb|Pais|1982|loc=ch. 16}} Yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between approximately 1960 and 1975, now known as the golden age of general relativity.BOOK, The future of theoretical physics and cosmology: celebrating Stephen Hawking's 60th birthday, Kip, Thorne, Cambridge University Press, 2003, 978-0-521-82081-3, 74,weblink harv, Extract of page 74 Physicists began to understand the concept of a black hole, and to identify quasars as one of these objects' astrophysical manifestations.{{Harvnb|Israel|1987|loc=ch. 7.8â€“7.10}}, {{Harvnb|Thorne|1994|loc=ch. 3â€“9}} Ever more precise solar system tests confirmed the theory's predictive power,Sections Orbital effects and the relativity of direction, Gravitational time dilation and frequency shift and Light deflection and gravitational time delay, and references therein and relativistic cosmology, too, became amenable to direct observational tests.Section Cosmology and references therein; the historical development is in {{Harvnb|Overbye|1999}}Over the years, general relativity has acquired a reputation as a theory of extraordinary beauty.{{Harvnb|Landau|Lifshitz|1975|loc=p. 228}} "...the general theory of relativity...was established by Einstein, and represents probably the most beautiful of all existing physical theories."{{Harvnb|Wald|1984|loc=p. 3}}{{Harvnb|Rovelli|2015|loc=pp. 1â€“6}} "General relativity is not just an extraordinarily beautiful physical theory providing the best description of the gravitational interaction we have so far. It is more." Subrahmanyan Chandrasekhar has noted that at multiple levels, general relativity exhibits what Francis Bacon has termed, a "strangeness in the proportion" (i.e. elements that excite wonderment and surprise). It juxtaposes fundamental concepts (space and time versus matter and motion) which had previously been considered as entirely independent. Chandrasekhar also noted that Einstein's only guides in his search for an exact theory were the principle of equivalence and his sense that a proper description of gravity should be geometrical at its basis, so that there was an "element of revelation" in the manner in which Einstein arrived at his theory.{{Harvnb|Chandrasekhar|1984|loc=p. 6}} Other elements of beauty associated with the general theory of relativity are its simplicity, symmetry, the manner in which it incorporates invariance and unification, and its perfect logical consistency.{{Harvnb|Engler|2002}}

## From classical mechanics to general relativity

General relativity can be understood by examining its similarities with and departures from classical physics. The first step is the realization that classical mechanics and Newton's law of gravity admit a geometric description. The combination of this description with the laws of special relativity results in a heuristic derivation of general relativity.The following exposition re-traces that of {{Harvnb|Ehlers|1973|loc=sec. 1}}

### Geometry of Newtonian gravity

(File:Elevator gravity.svg|thumb|According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure. For example, an observer will see a ball fall the same way in a rocket (left) as it does on Earth (right), provided that the acceleration of the rocket is equal to 9.8 m/s2 (the acceleration due to gravity at the surface of the Earth).)At the base of classical mechanics is the notion that a body's motion can be described as a combination of free (or inertial) motion, and deviations from this free motion. Such deviations are caused by external forces acting on a body in accordance with Newton's second law of motion, which states that the net force acting on a body is equal to that body's (inertial) mass multiplied by its acceleration.{{Harvnb|Arnold|1989|loc=ch. 1}} The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime.{{Harvnb|Ehlers|1973|pp=5f}}Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces (such as electromagnetism or friction), can be used to define the geometry of space, as well as a time coordinate. However, there is an ambiguity once gravity comes into play. According to Newton's law of gravity, and independently verified by experiments such as that of EÃ¶tvÃ¶s and its successors (see EÃ¶tvÃ¶s experiment), there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.{{Harvnb|Will|1993|loc=sec. 2.4}}, {{Harvnb|Will|2006|loc=sec. 2}} A simplified version of this is embodied in Einstein's elevator experiment, illustrated in the figure on the right: for an observer in a small enclosed room, it is impossible to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is at rest in a gravitational field, or in free space aboard a rocket that is accelerating at a rate equal to that of the gravitational field.{{Harvnb|Wheeler|1990|loc=ch. 2}}Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of the gravitational force. This suggests the definition of a new class of inertial motion, namely that of objects in free fall under the influence of gravity. This new class of preferred motions, too, defines a geometry of space and timeâ€”in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential. Space, in this construction, still has the ordinary Euclidean geometry. However, spacetime as a whole is more complicated. As can be shown using simple thought experiments following the free-fall trajectories of different test particles, the result of transporting spacetime vectors that can denote a particle's velocity (time-like vectors) will vary with the particle's trajectory; mathematically speaking, the Newtonian connection is not integrable. From this, one can deduce that spacetime is curved. The resulting Newtonâ€“Cartan theory is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system.{{Harvnb|Ehlers|1973|loc=sec. 1.2}}, {{Harvnb|Havas|1964}}, {{Harvnb|KÃ¼nzle|1972}}. The simple thought experiment in question was first described in {{Harvnb|Heckmann|SchÃ¼cking|1959}} In this geometric description, tidal effectsâ€”the relative acceleration of bodies in free fallâ€”are related to the derivative of the connection, showing how the modified geometry is caused by the presence of mass.{{Harvnb|Ehlers|1973|pp=10f}}

### Relativistic generalization

File:Light cone.svg|thumb|left|upright|Light coneLight coneAs intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics.Good introductions are, in order of increasing presupposed knowledge of mathematics, {{Harvnb|Giulini|2005}}, {{Harvnb|Mermin|2005}}, and {{Harvnb|Rindler|1991}}; for accounts of precision experiments, cf. part IV of {{Harvnb|Ehlers|LÃ¤mmerzahl|2006}} In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. (The defining symmetry of special relativity is the PoincarÃ© group, which includes translations, rotations and boosts.) The differences between the two become significant when dealing with speeds approaching the speed of light, and with high-energy phenomena.An in-depth comparison between the two symmetry groups can be found in {{Harvnb|Giulini|2006}}With Lorentz symmetry, additional structures come into play. They are defined by the set of light cones (see image). The light-cones define a causal structure: for each event {{math|A}}, there is a set of events that can, in principle, either influence or be influenced by {{math|A}} via signals or interactions that do not need to travel faster than light (such as event {{math|B}} in the image), and a set of events for which such an influence is impossible (such as event {{math|C}} in the image). These sets are observer-independent.{{Harvnb|Rindler|1991|loc=sec. 22}}, {{Harvnb|Synge|1972|loc=ch. 1 and 2}} In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the spaceâ€“time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure{{Harvnb|Ehlers|1973|loc=sec. 2.3}} or conformal geometry.Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames. Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.{{Harvnb|Ehlers|1973|loc=sec. 1.4}}, {{Harvnb|Schutz|1985|loc=sec. 5.1}}A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity holdâ€”that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames. But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field (cf. below). The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity.{{Harvnb|Ehlers|1973|pp=17ff}}; a derivation can be found in {{Harvnb|Mermin|2005|loc=ch. 12}}. For the experimental evidence, cf. the section Gravitational time dilation and frequency shift, below The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle, a crucial guiding principle for generalizing special-relativistic physics to include gravity.{{Harvnb|Rindler|2001|loc=sec. 1.13}}; for an elementary account, see {{Harvnb|Wheeler|1990|loc=ch. 2}}; there are, however, some differences between the modern version and Einstein's original concept used in the historical derivation of general relativity, cf. {{Harvnb|Norton|1985}}The same experimental data shows that time as measured by clocks in a gravitational fieldâ€”proper time, to give the technical termâ€”does not follow the rules of special relativity. In the language of spacetime geometry, it is not measured by the Minkowski metric. As in the Newtonian case, this is suggestive of a more general geometry. At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian. Consequently, we are now dealing with a curved generalization of Minkowski space. The metric tensor that defines the geometryâ€”in particular, how lengths and angles are measuredâ€”is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric. Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish).{{Harvnb|Ehlers|1973|loc=sec. 1.4}} for the experimental evidence, see once more section Gravitational time dilation and frequency shift. Choosing a different connection with non-zero torsion leads to a modified theory known as Einsteinâ€“Cartan theory

### Einstein's equations

Having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains. In Newtonian gravity, the source is mass. In special relativity, mass turns out to be part of a more general quantity called the energyâ€“momentum tensor, which includes both energy and momentum densities as well as stress: pressure and shear.{{Harvnb|Ehlers|1973|p=16}}, {{Harvnb|Kenyon|1990|loc=sec. 7.2}}, {{Harvnb|Weinberg|1972|loc=sec. 2.8}} Using the equivalence principle, this tensor is readily generalized to curved spacetime. Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely. In special relativity, conservation of energyâ€“momentum corresponds to the statement that the energyâ€“momentum tensor is divergence-free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry. With this additional conditionâ€”the covariant divergence of the energyâ€“momentum tensor, and hence of whatever is on the other side of the equation, is zeroâ€” the simplest set of equations are what are called Einstein's (field) equations:{{Equation box 1|indent=:|title=Einstein's field equations|equation=G_{munu}equiv R_{munu} - {textstyle 1 over 2}R,g_{munu} = {8 pi G over c^4} T_{munu},|cellpadding|border|border colour = #50C878|background colour = #ECFCF4}}On the left-hand side is the Einstein tensor, a specific divergence-free combination of the Ricci tensor R_{munu} and the metric. Where G_{munu} is symmetric. In particular,
R=g^{munu}R_{munu},
is the curvature scalar. The Ricci tensor itself is related to the more general Riemann curvature tensor as
R_{munu}={R^alpha}_{mualphanu}.,
On the right-hand side, T_{munu} is the energyâ€“momentum tensor. All tensors are written in abstract index notation.{{Harvnb|Ehlers|1973|pp=19â€“22}}; for similar derivations, see sections 1 and 2 of ch. 7 in {{Harvnb|Weinberg|1972}}. The Einstein tensor is the only divergence-free tensor that is a function of the metric coefficients, their first and second derivatives at most, and allows the spacetime of special relativity as a solution in the absence of sources of gravity, cf. {{Harvnb|Lovelock|1972}}. The tensors on both side are of second rank, that is, they can each be thought of as 4Ã—4 matrices, each of which contains ten independent terms; hence, the above represents ten coupled equations. The fact that, as a consequence of geometric relations known as Bianchi identities, the Einstein tensor satisfies a further four identities reduces these to six independent equations, e.g. {{Harvnb|Schutz|1985|loc=sec. 8.3}} Matching the theory's prediction to observational results for planetary orbits or, equivalently, assuring that the weak-gravity, low-speed limit is Newtonian mechanics, the proportionality constant can be fixed as kappa = frac{8pi G}{c^4}, where G is the gravitational constant and c the speed of light in vacuum.{{Harvnb|Kenyon|1990|loc=sec. 7.4}} When there is no matter present, so that the energyâ€“momentum tensor vanishes, the results are the vacuum Einstein equations,
R_{munu}=0.,
In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime. In other words, a freely moving or falling particle always moves along a geodesic.The geodesic equation is:
{d^2 x^mu over ds^2}+Gamma^mu {}_{alpha beta}{d x^alpha over ds}{d x^beta over ds}=0,
where s is a scalar parameter of motion (e.g. the proper time), and Gamma^mu {}_{alpha beta} are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) which is symmetric in the two lower indices. Greek indices may take the values: 0, 1, 2, 3 and the summation convention is used for repeated indices alpha and beta. The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this equation is analogous to Newton's laws of motion which likewise provide formulae for the acceleration of a particle. This equation of motion employs the Einstein notation, meaning that repeated indices are summed (i.e. from zero to three). The Christoffel symbols are functions of the four space-time coordinates, and so are independent of the velocity or acceleration or other characteristics of a test particle whose motion is described by the geodesic equation.

### Alternatives to general relativity

There are alternatives to general relativity built upon the same premises, which include additional rules and/or constraints, leading to different field equations. Examples are Whitehead's theory, Bransâ€“Dicke theory, teleparallelism, f(R) gravity and Einsteinâ€“Cartan theory.{{Harvnb|Brans|Dicke|1961}}, {{Harvnb|Weinberg|1972|loc=sec. 3 in ch. 7}}, {{Harvnb|Goenner|2004|loc=sec. 7.2}}, and {{Harvnb|Trautman|2006}}, respectively

## Definition and basic applications

{{See also|Mathematics of general relativity|Physical theories modified by general relativity}}The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building.

### Definition and basic properties

General relativity is a metric theory of gravitation. At its core are Einstein's equations, which describe the relation between the geometry of a four-dimensional pseudo-Riemannian manifold representing spacetime, and the energyâ€“momentum contained in that spacetime.{{Harvnb|Wald|1984|loc=ch. 4}},{{Harvnb|Weinberg|1972|loc=ch. 7}} or, in fact, any other textbook on general relativity Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow.At least approximately, cf. {{Harvnb|Poisson|2004}} The curvature is, in turn, caused by the energyâ€“momentum of matter. Paraphrasing the relativist John Archibald Wheeler, spacetime tells matter how to move; matter tells spacetime how to curve.{{Harvnb|Wheeler|1990|p=xi}}While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank-two tensor, the latter reduces to the former in certain limiting cases. For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation.{{Harvnb|Wald|1984|loc=sec. 4.4}}As it is constructed using tensors, general relativity exhibits general covariance: its lawsâ€”and further laws formulated within the general relativistic frameworkâ€”take on the same form in all coordinate systems.{{Harvnb|Wald|1984|loc=sec. 4.1}} Furthermore, the theory does not contain any invariant geometric background structures, i.e. it is background independent. It thus satisfies a more stringent general principle of relativity, namely that the laws of physics are the same for all observers.For the (conceptual and historical) difficulties in defining a general principle of relativity and separating it from the notion of general covariance, see {{Harvnb|Giulini|2007}} Locally, as expressed in the equivalence principle, spacetime is Minkowskian, and the laws of physics exhibit local Lorentz invariance.section 5 in ch. 12 of {{Harvnb|Weinberg|1972}}

### Model-building

The core concept of general-relativistic model-building is that of a solution of Einstein's equations. Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold (usually defined by giving the metric in specific coordinates), and specific matter fields defined on that manifold. Matter and geometry must satisfy Einstein's equations, so in particular, the matter's energyâ€“momentum tensor must be divergence-free. The matter must, of course, also satisfy whatever additional equations were imposed on its properties. In short, such a solution is a model universe that satisfies the laws of general relativity, and possibly additional laws governing whatever matter might be present.Introductory chapters of {{Harvnb|Stephani|Kramer|MacCallum|Hoenselaers|2003}}Einstein's equations are nonlinear partial differential equations and, as such, difficult to solve exactly.A review showing Einstein's equation in the broader context of other PDEs with physical significance is {{Harvnb|Geroch|1996}} Nevertheless, a number of exact solutions are known, although only a few have direct physical applications.For background information and a list of solutions, cf. {{Harvnb|Stephani|Kramer|MacCallum|Hoenselaers|2003}}; a more recent review can be found in {{Harvnb|MacCallum|2006}} The best-known exact solutions, and also those most interesting from a physics point of view, are the Schwarzschild solution, the Reissnerâ€“NordstrÃ¶m solution and the Kerr metric, each corresponding to a certain type of black hole in an otherwise empty universe,{{Harvnb|Chandrasekhar|1983|loc=ch. 3,5,6}} and the Friedmannâ€“LemaÃ®treâ€“Robertsonâ€“Walker and de Sitter universes, each describing an expanding cosmos.{{Harvnb|Narlikar|1993|loc=ch. 4, sec. 3.3}} Exact solutions of great theoretical interest include the GÃ¶del universe (which opens up the intriguing possibility of time travel in curved spacetimes), the Taub-NUT solution (a model universe that is homogeneous, but anisotropic), and anti-de Sitter space (which has recently come to prominence in the context of what is called the Maldacena conjecture).Brief descriptions of these and further interesting solutions can be found in {{Harvnb|Hawking|Ellis|1973|loc=ch. 5}}Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions. In the field of numerical relativity, powerful computers are employed to simulate the geometry of spacetime and to solve Einstein's equations for interesting situations such as two colliding black holes.{{Harvnb|Lehner|2002}} In principle, such methods may be applied to any system, given sufficient computer resources, and may address fundamental questions such as naked singularities. Approximate solutions may also be found by perturbation theories such as linearized gravityFor instance {{Harvnb|Wald|1984|loc=sec. 4.4}} and its generalization, the post-Newtonian expansion, both of which were developed by Einstein. The latter provides a systematic approach to solving for the geometry of a spacetime that contains a distribution of matter that moves slowly compared with the speed of light. The expansion involves a series of terms; the first terms represent Newtonian gravity, whereas the later terms represent ever smaller corrections to Newton's theory due to general relativity.{{Harvnb|Will|1993|loc=sec. 4.1 and 4.2}} An extension of this expansion is the parametrized post-Newtonian (PPN) formalism, which allows quantitative comparisons between the predictions of general relativity and alternative theories.{{Harvnb|Will|2006|loc=sec. 3.2}}, {{Harvnb|Will|1993|loc=ch. 4}}

## Consequences of Einstein's theory

General relativity has a number of physical consequences. Some follow directly from the theory's axioms, whereas others have become clear only in the course of many years of research that followed Einstein's initial publication.

### Gravitational time dilation and frequency shift

(File:Gravitational red-shifting.png|thumb|Schematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body)Assuming that the equivalence principle holds,{{Harvnb|Rindler|2001|pp=24â€“26 vs. pp. 236â€“237}} and {{Harvnb|Ohanian|Ruffini|1994|pp=164â€“172}}. Einstein derived these effects using the equivalence principle as early as 1907, cf. {{Harvnb|Einstein|1907}} and the description in {{Harvnb|Pais|1982|pp=196â€“198}} gravity influences the passage of time. Light sent down into a gravity well is blueshifted, whereas light sent in the opposite direction (i.e., climbing out of the gravity well) is redshifted; collectively, these two effects are known as the gravitational frequency shift. More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation.{{Harvnb|Rindler|2001|pp=24â€“26}}; {{Harvnb|Misner|Thorne|Wheeler|1973 |loc=Â§ 38.5}}Gravitational redshift has been measured in the laboratoryPoundâ€“Rebka experiment, see {{Harvnb|Pound|Rebka|1959}}, {{Harvnb|Pound|Rebka|1960}}; {{Harvnb|Pound|Snider|1964}}; a list of further experiments is given in {{Harvnb|Ohanian|Ruffini|1994|loc=table 4.1 on p. 186}} and using astronomical observations.{{Harvnb|Greenstein|Oke|Shipman|1971}}; the most recent and most accurate Sirius B measurements are published in {{Harvnb|Barstow, Bond et al.|2005}}. Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks,Starting with the Hafeleâ€“Keating experiment, {{Harvnb|Hafele|Keating|1972a}} and {{Harvnb|Hafele|Keating|1972b}}, and culminating in the Gravity Probe A experiment; an overview of experiments can be found in {{Harvnb|Ohanian|Ruffini|1994|loc=table 4.1 on p. 186}} while ongoing validation is provided as a side effect of the operation of the Global Positioning System (GPS).GPS is continually tested by comparing atomic clocks on the ground and aboard orbiting satellites; for an account of relativistic effects, see {{Harvnb|Ashby|2002}} and {{Harvnb|Ashby|2003}} Tests in stronger gravitational fields are provided by the observation of binary pulsars.{{Harvnb|Stairs|2003}} and {{Harvnb|Kramer|2004}} All results are in agreement with general relativity.General overviews can be found in section 2.1. of Will 2006; Will 2003, pp. 32â€“36; {{Harvnb|Ohanian|Ruffini|1994|loc=sec. 4.2}} However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.{{Harvnb|Ohanian|Ruffini|1994|pp=164â€“172}}

### Light deflection and gravitational time delay

(File:Light deflection.png|thumb|left|upright|Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray))General relativity predicts that the path of light will follow the curvature of spacetime as it passes near a star. This effect was initially confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun.Cf. {{Harvnb|Kennefick|2005}} for the classic early measurements by Arthur Eddington's expeditions. For an overview of more recent measurements, see {{Harvnb|Ohanian|Ruffini|1994|loc=ch. 4.3}}. For the most precise direct modern observations using quasars, cf. {{Harvnb|Shapiro|Davis|Lebach|Gregory|2004}}This and related predictions follow from the fact that light follows what is called a light-like or null geodesicâ€”a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity.This is not an independent axiom; it can be derived from Einstein's equations and the Maxwell Lagrangian using a WKB approximation, cf. {{Harvnb|Ehlers|1973|loc=sec. 5}} As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion),{{Harvnb|Blanchet|2006|loc=sec. 1.3}} several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light,{{Harvnb|Rindler|2001|loc=sec. 1.16}}; for the historical examples, {{Harvnb|Israel|1987|pp=202â€“204}}; in fact, Einstein published one such derivation as {{Harvnb|Einstein|1907}}. Such calculations tacitly assume that the geometry of space is Euclidean, cf. {{Harvnb|Ehlers|Rindler|1997}} the angle of deflection resulting from such calculations is only half the value given by general relativity.From the standpoint of Einstein's theory, these derivations take into account the effect of gravity on time, but not its consequences for the warping of space, cf. {{Harvnb|Rindler|2001|loc=sec. 11.11}}Closely related to light deflection is the gravitational time delay (or Shapiro delay), the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.For the Sun's gravitational field using radar signals reflected from planets such as Venus and Mercury, cf. {{Harvnb|Shapiro|1964}}, {{Harvnb|Weinberg|1972|loc=ch. 8, sec. 7}}; for signals actively sent back by space probes (transponder measurements), cf. {{Harvnb|Bertotti|Iess|Tortora|2003}}; for an overview, see {{Harvnb|Ohanian|Ruffini|1994|loc=table 4.4 on p. 200}}; for more recent measurements using signals received from a pulsar that is part of a binary system, the gravitational field causing the time delay being that of the other pulsar, cf. {{Harvnb|Stairs|2003|loc=sec. 4.4}} In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called Î³, which encodes the influence of gravity on the geometry of space.{{Harvnb|Will|1993|loc=sec. 7.1 and 7.2}}{{clear}}

### Orbital effects and the relativity of direction

General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies. It predicts an overall rotation (precession) of planetary orbits, as well as orbital decay caused by the emission of gravitational waves and effects related to the relativity of direction.

#### Precession of apsides

(File:Relativistic precession.svg|thumb|Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star)In general relativity, the apsides of any orbit (the point of the orbiting body's closest approach to the system's center of mass) will precess; the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a test particle. For him, the fact that his theory gave a straightforward explanation of Mercury's anomalous perihelion shift, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.{{Harvnb|Schutz|2003|pp=48â€“49}}, {{Harvnb|Pais|1982|pp=253â€“254}}The effect can also be derived by using either the exact Schwarzschild metric (describing spacetime around a spherical mass){{Harvnb|Rindler|2001|loc=sec. 11.9}} or the much more general post-Newtonian formalism.{{Harvnb|Will|1993|pp=177â€“181}} It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body's gravity (encoded in the nonlinearity of Einstein's equations).In consequence, in the parameterized post-Newtonian formalism (PPN), measurements of this effect determine a linear combination of the terms Î² and Î³, cf. {{Harvnb|Will|2006|loc=sec. 3.5}} and {{Harvnb|Will|1993|loc=sec. 7.3}} Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus, and Earth),The most precise measurements are VLBI measurements of planetary positions; see {{Harvnb|Will|1993|loc=ch. 5}}, {{Harvnb|Will|2006|loc=sec. 3.5}}, {{Harvnb|Anderson|Campbell|Jurgens|Lau|1992}}; for an overview, {{Harvnb|Ohanian|Ruffini|1994|pp=406â€“407}} as well as in binary pulsar systems, where it is larger by five orders of magnitude.{{Harvnb|Kramer|Stairs|Manchester|McLaughlin|2006}}In general relativity the perihelion shift sigma, expressed in radians per revolution, is approximately given byBOOK, Theory and Practice of Natural Computing: Fourth International Conference, TPNC 2015, Mieres, Spain, December 15â€“16, 2015. Proceedings, illustrated, Adrian-Horia, Dediu, Luis, Magdalena, Carlos, MartÃ­n-Vide, Springer, 2015, 978-3-319-26841-5, 141,weblink Extract of page 141
sigma=frac {24pi^3L^2} {T^2c^2(1-e^2)} ,
where:

#### Orbital decay

(File:Psr1913+16-weisberg en.png|thumb|Orbital decay for PSR1913+16: time shift in seconds, tracked over three decades.A figure that includes error bars is fig. 7 in {{Harvnb|Will|2006|loc=sec. 5.1}})According to general relativity, a binary system will emit gravitational waves, thereby losing energy. Due to this loss, the distance between the two orbiting bodies decreases, and so does their orbital period. Within the Solar System or for ordinary double stars, the effect is too small to be observable. This is not the case for a close binary pulsar, a system of two orbiting neutron stars, one of which is a pulsar: from the pulsar, observers on Earth receive a regular series of radio pulses that can serve as a highly accurate clock, which allows precise measurements of the orbital period. Because neutron stars are immensely compact, significant amounts of energy are emitted in the form of gravitational radiation.{{Harvnb|Stairs|2003}}, {{Harvnb|Schutz|2003|pp=317â€“321}}, {{Harvnb|Bartusiak|2000|pp=70â€“86}}The first observation of a decrease in orbital period due to the emission of gravitational waves was made by Hulse and Taylor, using the binary pulsar PSR1913+16 they had discovered in 1974. This was the first detection of gravitational waves, albeit indirect, for which they were awarded the 1993 Nobel Prize in physics.{{Harvnb|Weisberg|Taylor|2003}}; for the pulsar discovery, see {{Harvnb|Hulse|Taylor|1975}}; for the initial evidence for gravitational radiation, see {{Harvnb|Taylor|1994}} Since then, several other binary pulsars have been found, in particular the double pulsar PSR J0737-3039, in which both stars are pulsars.{{Harvnb|Kramer|2004}}

#### Geodetic precession and frame-dragging

Several relativistic effects are directly related to the relativity of direction.{{Harvnb|Penrose|2004|loc=Â§14.5}}, {{Harvnb|Misner|Thorne|Wheeler|1973|loc=Â§11.4}} One is geodetic precession: the axis direction of a gyroscope in free fall in curved spacetime will change when compared, for instance, with the direction of light received from distant starsâ€”even though such a gyroscope represents the way of keeping a direction as stable as possible ("parallel transport").{{Harvnb|Weinberg|1972|loc=sec. 9.6}}, {{Harvnb|Ohanian|Ruffini|1994|loc=sec. 7.8}} For the Moonâ€“Earth system, this effect has been measured with the help of lunar laser ranging.{{Harvnb|Bertotti|Ciufolini|Bender|1987}}, {{Harvnb|Nordtvedt|2003}} More recently, it has been measured for test masses aboard the satellite Gravity Probe B to a precision of better than 0.3%.{{Harvnb|Kahn|2007}}A mission description can be found in {{Harvnb|Everitt|Buchman|DeBra|Keiser|2001}}; a first post-flight evaluation is given in {{Harvnb|Everitt|Parkinson|Kahn|2007}}; further updates will be available on the mission website {{Harvnb|Kahn|1996â€“2012}}.Near a rotating mass, there are gravitomagnetic or frame-dragging effects. A distant observer will determine that objects close to the mass get "dragged around". This is most extreme for rotating black holes where, for any object entering a zone known as the ergosphere, rotation is inevitable.{{Harvnb|Townsend|1997|loc=sec. 4.2.1}}, {{Harvnb|Ohanian|Ruffini|1994|pp=469â€“471}} Such effects can again be tested through their influence on the orientation of gyroscopes in free fall.{{Harvnb|Ohanian|Ruffini|1994|loc=sec. 4.7}}, {{Harvnb|Weinberg|1972|loc=sec. 9.7}}; for a more recent review, see {{Harvnb|SchÃ¤fer|2004}} Somewhat controversial tests have been performed using the LAGEOS satellites, confirming the relativistic prediction.{{Harvnb|Ciufolini|Pavlis|2004}}, {{Harvnb|Ciufolini|Pavlis|Peron|2006}}, {{Harvnb|Iorio|2009}} Also the Mars Global Surveyor probe around Mars has been used.{{Citation| author=Iorio L.|title=COMMENTS, REPLIES AND NOTES: A note on the evidence of the gravitomagnetic field of Mars |date=August 2006| journal=Classical and Quantum Gravity|volume=23| issue=17| pages=5451â€“5454|doi=10.1088/0264-9381/23/17/N01|arxiv = gr-qc/0606092 |bibcode = 2006CQGra..23.5451I }}{{Citation| author=Iorio L.|title=On the Lenseâ€“Thirring test with the Mars Global Surveyor in the gravitational field of Mars| journal=Central European Journal of Physics |date=June 2010| doi=10.2478/s11534-009-0117-6|volume= 8 |issue =3 |pages= 509â€“513|arxiv = gr-qc/0701146 |bibcode = 2010CEJPh...8..509I }}

## Astrophysical applications

### Gravitational lensing

File:Einstein cross.jpg|thumb|(Einstein cross]]: four images of the same astronomical object, produced by a gravitational lens)The deflection of light by gravity is responsible for a new class of astronomical phenomena. If a massive object is situated between the astronomer and a distant target object with appropriate mass and relative distances, the astronomer will see multiple distorted images of the target. Such effects are known as gravitational lensing.For overviews of gravitational lensing and its applications, see {{Harvnb|Ehlers|Falco|Schneider|1992}} and {{Harvnb|Wambsganss|1998}} Depending on the configuration, scale, and mass distribution, there can be two or more images, a bright ring known as an Einstein ring, or partial rings called arcs.For a simple derivation, see {{Harvnb|Schutz|2003|loc=ch. 23}}; cf. {{Harvnb|Narayan|Bartelmann|1997|loc=sec. 3}}The earliest example was discovered in 1979;{{Harvnb|Walsh|Carswell|Weymann|1979}} since then, more than a hundred gravitational lenses have been observed.Images of all the known lenses can be found on the pages of the CASTLES project, {{Harvnb|Kochanek|Falco|Impey|Lehar|2007}} Even if the multiple images are too close to each other to be resolved, the effect can still be measured, e.g., as an overall brightening of the target object; a number of such "microlensing events" have been observed.{{Harvnb|Roulet|Mollerach|1997}}Gravitational lensing has developed into a tool of observational astronomy. It is used to detect the presence and distribution of dark matter, provide a "natural telescope" for observing distant galaxies, and to obtain an independent estimate of the Hubble constant. Statistical evaluations of lensing data provide valuable insight into the structural evolution of galaxies.{{Harvnb|Narayan|Bartelmann|1997|loc=sec. 3.7}}

### Gravitational wave astronomy

File:LISA.jpg|thumb|180px|Artist's impression of the space-borne gravitational wave detector LISA ]]Observations of binary pulsars provide strong indirect evidence for the existence of gravitational waves (see Orbital decay, above). Detection of these waves is a major goal of current relativity-related research.{{Harvnb|Barish|2005}}, {{Harvnb|Bartusiak|2000}}, {{Harvnb|Blair|McNamara|1997}} Several land-based gravitational wave detectors are currently in operation, most notably the interferometric detectors GEO 600, LIGO (two detectors), TAMA 300 and VIRGO.{{Harvnb|Hough|Rowan|2000}} Various pulsar timing arrays are using millisecond pulsars to detect gravitational waves in the 10âˆ’9 to 10âˆ’6 Hertz frequency range, which originate from binary supermassive blackholes.{{Citation | last1=Hobbs | first1=George |title=The international pulsar timing array project: using pulsars as a gravitational wave detector | last2=Archibald | first2=A. | last3=Arzoumanian | first3=Z. | last4=Backer | first4=D. | last5=Bailes | first5=M. | last6=Bhat | first6=N. D. R. | last7=Burgay | first7=M. | last8=Burke-Spolaor | first8=S. | last9=Champion | first9=D. | displayauthors = 8| doi=10.1088/0264-9381/27/8/084013 | date=2010 | journal=Classical and Quantum Gravity | volume=27 | issue=8 | page=084013 |arxiv=0911.5206 |bibcode = 2010CQGra..27h4013H }} A European space-based detector, eLISA / NGO, is currently under development,{{Harvnb|Danzmann|RÃ¼diger|2003}} with a precursor mission (LISA Pathfinder) having launched in December 2015.WEB,weblink LISA pathfinder overview, ESA, 2012-04-23, Observations of gravitational waves promise to complement observations in the electromagnetic spectrum.{{Harvnb|Thorne|1995}} They are expected to yield information about black holes and other dense objects such as neutron stars and white dwarfs, about certain kinds of supernova implosions, and about processes in the very early universe, including the signature of certain types of hypothetical cosmic string.{{Harvnb|Cutler|Thorne|2002}} In February 2016, the Advanced LIGO team announced that they had detected gravitational waves from a black hole merger.

### Black holes and other compact objects

Whenever the ratio of an object's mass to its radius becomes sufficiently large, general relativity predicts the formation of a black hole, a region of space from which nothing, not even light, can escape. In the currently accepted models of stellar evolution, neutron stars of around 1.4 solar masses, and stellar black holes with a few to a few dozen solar masses, are thought to be the final state for the evolution of massive stars.{{Harvnb|Miller|2002|loc=lectures 19 and 21}} Usually a galaxy has one supermassive black hole with a few million to a few billion solar masses in its center,{{Harvnb|Celotti|Miller|Sciama|1999|loc=sec. 3}} and its presence is thought to have played an important role in the formation of the galaxy and larger cosmic structures.{{Harvnb|Springel|White|Jenkins|Frenk|2005}} and the accompanying summary {{Harvnb|Gnedin|2005}}(File:Star collapse to black hole.png|thumb|left|Simulation based on the equations of general relativity: a star collapsing to form a black hole while emitting gravitational waves)Astronomically, the most important property of compact objects is that they provide a supremely efficient mechanism for converting gravitational energy into electromagnetic radiation.{{Harvnb|Blandford|1987|loc=sec. 8.2.4}} Accretion, the falling of dust or gaseous matter onto stellar or supermassive black holes, is thought to be responsible for some spectacularly luminous astronomical objects, notably diverse kinds of active galactic nuclei on galactic scales and stellar-size objects such as microquasars.For the basic mechanism, see {{Harvnb|Carroll|Ostlie|1996|loc=sec. 17.2}}; for more about the different types of astronomical objects associated with this, cf. {{Harvnb|Robson|1996}} In particular, accretion can lead to relativistic jets, focused beams of highly energetic particles that are being flung into space at almost light speed.For a review, see {{Harvnb|Begelman|Blandford|Rees|1984}}. To a distant observer, some of these jets even appear to move faster than light; this, however, can be explained as an optical illusion that does not violate the tenets of relativity, see {{Harvnb|Rees|1966}}General relativity plays a central role in modelling all these phenomena,For stellar end states, cf. {{Harvnb|Oppenheimer|Snyder|1939}} or, for more recent numerical work, {{Harvnb|Font|2003|loc=sec. 4.1}}; for supernovae, there are still major problems to be solved, cf. {{Harvnb|Buras|Rampp|Janka|Kifonidis|2003}}; for simulating accretion and the formation of jets, cf. {{Harvnb|Font|2003|loc=sec. 4.2}}. Also, relativistic lensing effects are thought to play a role for the signals received from X-ray pulsars, cf. {{Harvnb|Kraus|1998}} and observations provide strong evidence for the existence of black holes with the properties predicted by the theory.The evidence includes limits on compactness from the observation of accretion-driven phenomena ("Eddington luminosity"), see {{Harvnb|Celotti|Miller|Sciama|1999}}, observations of stellar dynamics in the center of our own Milky Way galaxy, cf. {{Harvnb|SchÃ¶del|Ott|Genzel|Eckart|2003}}, and indications that at least some of the compact objects in question appear to have no solid surface, which can be deduced from the examination of X-ray bursts for which the central compact object is either a neutron star or a black hole; cf. {{Harvnb|Remillard|Lin|Cooper|Narayan|2006}} for an overview, {{Harvnb|Narayan|2006|loc=sec. 5}}. Observations of the "shadow" of the Milky Way galaxy's central black hole horizon are eagerly sought for, cf. {{Harvnb|Falcke|Melia|Agol|2000}}Black holes are also sought-after targets in the search for gravitational waves (cf. Gravitational waves, above). Merging black hole binaries should lead to some of the strongest gravitational wave signals reaching detectors here on Earth, and the phase directly before the merger ("chirp") could be used as a "standard candle" to deduce the distance to the merger eventsâ€“and hence serve as a probe of cosmic expansion at large distances.{{Harvnb|Dalal|Holz|Hughes|Jain|2006}} The gravitational waves produced as a stellar black hole plunges into a supermassive one should provide direct information about the supermassive black hole's geometry.{{Harvnb|Barack|Cutler|2004}}{{clear}}

### Cosmology

File:Lensshoe hubble.jpg|thumb|This blue horseshoe is a distant galaxy that has been magnified and warped into a nearly complete ring by the strong gravitational pull of the massive foreground luminous red galaxy.]]The current models of cosmology are based on Einstein's field equations, which include the cosmological constant Lambda since it has important influence on the large-scale dynamics of the cosmos,
R_{munu} - {textstyle 1 over 2}R,g_{munu} + Lambda g_{munu} = frac{8pi G}{c^{4}}, T_{munu}

### Time travel

Kurt GÃ¶del showed{{harvnb|GÃ¶del|1949}} that solutions to Einstein's equations exist that contain closed timelike curves (CTCs), which allow for loops in time. The solutions require extreme physical conditions unlikely ever to occur in practice, and it remains an open question whether further laws of physics will eliminate them completely. Since then, otherâ€”similarly impracticalâ€”GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes.

### Causal structure and global geometry

File:Penrose.svg|thumb|Penroseâ€“Carter diagram of an infinite Minkowski universe ]]In general relativity, no material body can catch up with or overtake a light pulse. No influence from an event A can reach any other location X before light sent out at A to X. In consequence, an exploration of all light worldlines (null geodesics) yields key information about the spacetime's causal structure. This structure can be displayed using Penroseâ€“Carter diagrams in which infinitely large regions of space and infinite time intervals are shrunk ("compactified") so as to fit onto a finite map, while light still travels along diagonals as in standard spacetime diagrams.{{Harvnb|Frauendiener|2004}}, {{Harvnb|Wald|1984|loc=sec. 11.1}}, {{Harvnb|Hawking|Ellis|1973|loc=sec. 6.8, 6.9}}Aware of the importance of causal structure, Roger Penrose and others developed what is known as global geometry. In global geometry, the object of study is not one particular solution (or family of solutions) to Einstein's equations. Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter (usually in the form of energy conditions) are used to derive general results.{{Harvnb|Wald|1984|loc=sec. 9.2â€“9.4}} and {{Harvnb|Hawking|Ellis|1973|loc=ch. 6}}

### Horizons

Using global geometry, some spacetimes can be shown to contain boundaries called horizons, which demarcate one region from the rest of spacetime. The best-known examples are black holes: if mass is compressed into a sufficiently compact region of space (as specified in the hoop conjecture, the relevant length scale is the Schwarzschild radius{{Harvnb|Thorne|1972}}; for more recent numerical studies, see {{Harvnb|Berger|2002|loc=sec. 2.1}}), no light from inside can escape to the outside. Since no object can overtake a light pulse, all interior matter is imprisoned as well. Passage from the exterior to the interior is still possible, showing that the boundary, the black hole's horizon, is not a physical barrier.{{Harvnb|Israel|1987}}. A more exact mathematical description distinguishes several kinds of horizon, notably event horizons and apparent horizons cf. {{Harvnb|Hawking|Ellis|1973|pp=312â€“320}} or {{Harvnb|Wald|1984|loc=sec. 12.2}}; there are also more intuitive definitions for isolated systems that do not require knowledge of spacetime properties at infinity, cf. {{Harvnb|Ashtekar|Krishnan|2004}}(File:Ergosphere.svg|thumb|left|The ergosphere of a rotating black hole, which plays a key role when it comes to extracting energy from such a black hole)Early studies of black holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a static black hole) and the axisymmetric Kerr solution (used to describe a rotating, stationary black hole, and introducing interesting features such as the ergosphere). Using global geometry, later studies have revealed more general properties of black holes. With time they become rather simple objects characterized by eleven parameters specifying: electric charge, mass-energy, linear momentum, angular momentum, and location at a specified time. This is stated by the black hole uniqueness theorem: "black holes have no hair", that is, no distinguishing marks like the hairstyles of humans. Irrespective of the complexity of a gravitating object collapsing to form a black hole, the object that results (having emitted gravitational waves) is very simple.For first steps, cf. {{Harvnb|Israel|1971}}; see {{Harvnb|Hawking|Ellis|1973|loc=sec. 9.3}} or {{Harvnb|Heusler|1996|loc=ch. 9 and 10}} for a derivation, and {{Harvnb|Heusler|1998}} as well as {{Harvnb|Beig|ChruÅ›ciel|2006}} as overviews of more recent resultsEven more remarkably, there is a general set of laws known as black hole mechanics, which is analogous to the laws of thermodynamics. For instance, by the second law of black hole mechanics, the area of the event horizon of a general black hole will never decrease with time, analogous to the entropy of a thermodynamic system. This limits the energy that can be extracted by classical means from a rotating black hole (e.g. by the Penrose process).The laws of black hole mechanics were first described in {{Harvnb|Bardeen|Carter|Hawking|1973}}; a more pedagogical presentation can be found in {{Harvnb|Carter|1979}}; for a more recent review, see {{Harvnb|Wald|2001|loc=ch. 2}}. A thorough, book-length introduction including an introduction to the necessary mathematics {{Harvnb|Poisson|2004}}. For the Penrose process, see {{Harvnb|Penrose|1969}} There is strong evidence that the laws of black hole mechanics are, in fact, a subset of the laws of thermodynamics, and that the black hole area is proportional to its entropy.{{Harvnb|Bekenstein|1973}}, {{Harvnb|Bekenstein|1974}} This leads to a modification of the original laws of black hole mechanics: for instance, as the second law of black hole mechanics becomes part of the second law of thermodynamics, it is possible for black hole area to decreaseâ€”as long as other processes ensure that, overall, entropy increases. As thermodynamical objects with non-zero temperature, black holes should emit thermal radiation. Semi-classical calculations indicate that indeed they do, with the surface gravity playing the role of temperature in Planck's law. This radiation is known as Hawking radiation (cf. the quantum theory section, below).The fact that black holes radiate, quantum mechanically, was first derived in {{Harvnb|Hawking|1975}}; a more thorough derivation can be found in {{Harvnb|Wald|1975}}. A review is given in {{Harvnb|Wald|2001|loc=ch. 3}}There are other types of horizons. In an expanding universe, an observer may find that some regions of the past cannot be observed ("particle horizon"), and some regions of the future cannot be influenced (event horizon).{{Harvnb|Narlikar|1993|loc=sec. 4.4.4, 4.4.5}} Even in flat Minkowski space, when described by an accelerated observer (Rindler space), there will be horizons associated with a semi-classical radiation known as Unruh radiation.Horizons: cf. {{Harvnb|Rindler|2001|loc=sec. 12.4}}. Unruh effect: {{Harvnb|Unruh|1976}}, cf. {{Harvnb|Wald|2001|loc=ch. 3}}

### Singularities

Another general feature of general relativity is the appearance of spacetime boundaries known as singularities. Spacetime can be explored by following up on timelike and lightlike geodesicsâ€”all possible ways that light and particles in free fall can travel. But some solutions of Einstein's equations have "ragged edges"â€”regions known as spacetime singularities, where the paths of light and falling particles come to an abrupt end, and geometry becomes ill-defined. In the more interesting cases, these are "curvature singularities", where geometrical quantities characterizing spacetime curvature, such as the Ricci scalar, take on infinite values.{{Harvnb|Hawking|Ellis|1973|loc=sec. 8.1}}, {{Harvnb|Wald|1984|loc=sec. 9.1}} Well-known examples of spacetimes with future singularitiesâ€”where worldlines endâ€”are the Schwarzschild solution, which describes a singularity inside an eternal static black hole,{{Harvnb|Townsend|1997|loc=ch. 2}}; a more extensive treatment of this solution can be found in {{Harvnb|Chandrasekhar|1983|loc=ch. 3}} or the Kerr solution with its ring-shaped singularity inside an eternal rotating black hole.{{Harvnb|Townsend|1997|loc=ch. 4}}; for a more extensive treatment, cf. {{Harvnb|Chandrasekhar|1983|loc=ch. 6}} The Friedmannâ€“LemaÃ®treâ€“Robertsonâ€“Walker solutions and other spacetimes describing universes have past singularities on which worldlines begin, namely Big Bang singularities, and some have future singularities (Big Crunch) as well.{{Harvnb|Ellis|Van Elst|1999}}; a closer look at the singularity itself is taken in {{Harvnb|BÃ¶rner|1993|loc=sec. 1.2}}Given that these examples are all highly symmetricâ€”and thus simplifiedâ€”it is tempting to conclude that the occurrence of singularities is an artifact of idealization.Here one should remind to the well-known fact that the important "quasi-optical" singularities of the so-called eikonal approximations of many wave-equations, namely the "caustics", are resolved into finite peaks beyond that approximation. The famous singularity theorems, proved using the methods of global geometry, say otherwise: singularities are a generic feature of general relativity, and unavoidable once the collapse of an object with realistic matter properties has proceeded beyond a certain stageNamely when there are trapped null surfaces, cf. {{Harvnb|Penrose|1965}} and also at the beginning of a wide class of expanding universes.{{Harvnb|Hawking|1966}} However, the theorems say little about the properties of singularities, and much of current research is devoted to characterizing these entities' generic structure (hypothesized e.g. by the BKL conjecture).The conjecture was made in {{Harvnb|Belinskii|Khalatnikov|Lifschitz|1971}}; for a more recent review, see {{Harvnb|Berger|2002}}. An accessible exposition is given by {{Harvnb|Garfinkle|2007}} The cosmic censorship hypothesis states that all realistic future singularities (no perfect symmetries, matter with realistic properties) are safely hidden away behind a horizon, and thus invisible to all distant observers. While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.The restriction to future singularities naturally excludes initial singularities such as the big bang singularity, which in principle be visible to observers at later cosmic time. The cosmic censorship conjecture was first presented in {{Harvnb|Penrose|1969}}; a textbook-level account is given in {{Harvnb|Wald|1984|pp=302â€“305}}. For numerical results, see the review {{Harvnb|Berger|2002|loc=sec. 2.1}}

### Evolution equations

Each solution of Einstein's equation encompasses the whole history of a universe â€” it is not just some snapshot of how things are, but a whole, possibly matter-filled, spacetime. It describes the state of matter and geometry everywhere and at every moment in that particular universe. Due to its general covariance, Einstein's theory is not sufficient by itself to determine the time evolution of the metric tensor. It must be combined with a coordinate condition, which is analogous to gauge fixing in other field theories.{{Harvnb|Hawking|Ellis|1973|loc=sec. 7.1}}To understand Einstein's equations as partial differential equations, it is helpful to formulate them in a way that describes the evolution of the universe over time. This is done in "3+1" formulations, where spacetime is split into three space dimensions and one time dimension. The best-known example is the ADM formalism.{{Harvnb|Arnowitt|Deser|Misner|1962}}; for a pedagogical introduction, see {{Harvnb|Misner|Thorne|Wheeler|1973|loc=Â§21.4â€“Â§21.7}} These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist, and are uniquely defined, once suitable initial conditions have been specified.{{Harvnb|FourÃ¨s-Bruhat|1952}} and {{Harvnb|Bruhat|1962}}; for a pedagogical introduction, see {{Harvnb|Wald|1984|loc=ch. 10}}; an online review can be found in {{Harvnb|Reula|1998}} Such formulations of Einstein's field equations are the basis of numerical relativity.{{Harvnb|Gourgoulhon|2007}}; for a review of the basics of numerical relativity, including the problems arising from the peculiarities of Einstein's equations, see {{Harvnb|Lehner|2001}}

### Global and quasi-local quantities

The notion of evolution equations is intimately tied in with another aspect of general relativistic physics. In Einstein's theory, it turns out to be impossible to find a general definition for a seemingly simple property such as a system's total mass (or energy). The main reason is that the gravitational fieldâ€”like any physical fieldâ€”must be ascribed a certain energy, but that it proves to be fundamentally impossible to localize that energy.{{Harvnb|Misner|Thorne|Wheeler|1973|loc=Â§20.4}}Nevertheless, there are possibilities to define a system's total mass, either using a hypothetical "infinitely distant observer" (ADM mass){{Harvnb|Arnowitt|Deser|Misner|1962}} or suitable symmetries (Komar mass).{{Harvnb|Komar|1959}}; for a pedagogical introduction, see {{Harvnb|Wald|1984|loc=sec. 11.2}}; although defined in a totally different way, it can be shown to be equivalent to the ADM mass for stationary spacetimes, cf. {{Harvnb|Ashtekar|Magnon-Ashtekar|1979}} If one excludes from the system's total mass the energy being carried away to infinity by gravitational waves, the result is the Bondi mass at null infinity.For a pedagogical introduction, see {{Harvnb|Wald|1984|loc=sec. 11.2}} Just as in classical physics, it can be shown that these masses are positive.{{Harvnb|Wald|1984|p=295 and refs therein}}; this is important for questions of stabilityâ€”if there were negative mass states, then flat, empty Minkowski space, which has mass zero, could evolve into these states Corresponding global definitions exist for momentum and angular momentum.{{Harvnb|Townsend|1997|loc=ch. 5}} There have also been a number of attempts to define quasi-local quantities, such as the mass of an isolated system formulated using only quantities defined within a finite region of space containing that system. The hope is to obtain a quantity useful for general statements about isolated systems, such as a more precise formulation of the hoop conjecture.Such quasi-local massâ€“energy definitions are the Hawking energy, Geroch energy, or Penrose's quasi-local energyâ€“momentum based on twistor methods; cf. the review article {{Harvnb|Szabados|2004}}

## Relationship with quantum theory

If general relativity were considered to be one of the two pillars of modern physics, then quantum theory, the basis of understanding matter from elementary particles to solid state physics, would be the other.An overview of quantum theory can be found in standard textbooks such as {{Harvnb|Messiah|1999}}; a more elementary account is given in {{Harvnb|Hey|Walters|2003}} However, how to reconcile quantum theory with general relativity is still an open question.

### Quantum field theory in curved spacetime

Ordinary quantum field theories, which form the basis of modern elementary particle physics, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth.{{Harvnb|Ramond|1990}}, {{Harvnb|Weinberg|1995}}, {{Harvnb|Peskin|Schroeder|1995}}; a more accessible overview is {{Harvnb|Auyang|1995}} In order to describe situations in which gravity is strong enough to influence (quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime. These theories rely on general relativity to describe a curved background spacetime, and define a generalized quantum field theory to describe the behavior of quantum matter within that spacetime.{{Harvnb|Wald|1994}}, {{Harvnb|Birrell|Davies|1984}} Using this formalism, it can be shown that black holes emit a blackbody spectrum of particles known as Hawking radiation leading to the possibility that they evaporate over time.For Hawking radiation {{Harvnb|Hawking|1975}}, {{Harvnb|Wald|1975}}; an accessible introduction to black hole evaporation can be found in {{Harvnb|Traschen|2000}} As briefly mentioned above, this radiation plays an important role for the thermodynamics of black holes.{{Harvnb|Wald|2001|loc=ch. 3}}

### Quantum gravity

{{See also|String theory|Canonical general relativity|Loop quantum gravity|Causal Dynamical Triangulations|Causal sets}}The demand for consistency between a quantum description of matter and a geometric description of spacetime,Put simply, matter is the source of spacetime curvature, and once matter has quantum properties, we can expect spacetime to have them as well. Cf. {{Harvnb|Carlip|2001|loc=sec. 2}} as well as the appearance of singularities (where curvature length scales become microscopic), indicate the need for a full theory of quantum gravity: for an adequate description of the interior of black holes, and of the very early universe, a theory is required in which gravity and the associated geometry of spacetime are described in the language of quantum physics.{{Harvnb|Schutz|2003|p=407}} Despite major efforts, no complete and consistent theory of quantum gravity is currently known, even though a number of promising candidates exist.{{Harvnb|Hamber|2009}}A timeline and overview can be found in {{Harvnb|Rovelli|2000}}
missing image!
- Calabi yau.jpg -
Projection of a Calabiâ€“Yau manifold, one of the ways of compactifying the extra dimensions posited by string theory
Attempts to generalize ordinary quantum field theories, used in elementary particle physics to describe fundamental interactions, so as to include gravity have led to serious problems.{{Harvnb|'t Hooft|Veltman|1974}} Some have argued that at low energies, this approach proves successful, in that it results in an acceptable effective (quantum) field theory of gravity.{{Harvnb|Donoghue|1995}} At very high energies, however, the perturbative results are badly divergent and lead to models devoid of predictive power ("perturbative non-renormalizability").In particular, a perturbative technique known as renormalization, an integral part of deriving predictions which take into account higher-energy contributions, cf. {{Harvnb|Weinberg|1996|loc=ch. 17, 18}}, fails in this case; cf. {{Harvnb|Veltman|1975}}, {{Harvnb|Goroff|Sagnotti|1985}}; for a recent comprehensive review of the failure of perturbative renormalizability for quantum gravity see {{Harvnb|Hamber|2009}}File:Spin network.svg|thumb|Simple spin networkspin networkOne attempt to overcome these limitations is string theory, a quantum theory not of point particles, but of minute one-dimensional extended objects.An accessible introduction at the undergraduate level can be found in {{Harvnb|Zwiebach|2004}}; more complete overviews can be found in {{Harvnb|Polchinski|1998a}} and {{Harvnb|Polchinski|1998b}} The theory promises to be a unified description of all particles and interactions, including gravity;At the energies reached in current experiments, these strings are indistinguishable from point-like particles, but, crucially, different modes of oscillation of one and the same type of fundamental string appear as particles with different (electric and other) charges, e.g. {{Harvnb|Ibanez|2000}}. The theory is successful in that one mode will always correspond to a graviton, the messenger particle of gravity, e.g. {{Harvnb|Green|Schwarz|Witten|1987|loc=sec. 2.3, 5.3}} the price to pay is unusual features such as six extra dimensions of space in addition to the usual three.{{Harvnb|Green|Schwarz|Witten|1987|loc=sec. 4.2}} In what is called the second superstring revolution, it was conjectured that both string theory and a unification of general relativity and supersymmetry known as supergravity{{Harvnb|Weinberg|2000|loc=ch. 31}} form part of a hypothesized eleven-dimensional model known as M-theory, which would constitute a uniquely defined and consistent theory of quantum gravity.{{Harvnb|Townsend|1996}}, {{Harvnb|Duff|1996}}Another approach starts with the canonical quantization procedures of quantum theory. Using the initial-value-formulation of general relativity (cf. evolution equations above), the result is the Wheelerâ€“deWitt equation (an analogue of the SchrÃ¶dinger equation) which, regrettably, turns out to be ill-defined without a proper ultraviolet (lattice) cutoff.{{Harvnb|KuchaÅ™|1973|loc=sec. 3}} However, with the introduction of what are now known as Ashtekar variables,These variables represent geometric gravity using mathematical analogues of electric and magnetic fields; cf. {{Harvnb|Ashtekar|1986}}, {{Harvnb|Ashtekar|1987}} this leads to a promising model known as loop quantum gravity. Space is represented by a web-like structure called a spin network, evolving over time in discrete steps.For a review, see {{Harvnb|Thiemann|2007}}; more extensive accounts can be found in {{Harvnb|Rovelli|1998}}, {{Harvnb|Ashtekar|Lewandowski|2004}} as well as in the lecture notes {{Harvnb|Thiemann|2003}}Depending on which features of general relativity and quantum theory are accepted unchanged, and on what level changes are introduced,{{Harvnb|Isham|1994}}, {{Harvnb|Sorkin|1997}} there are numerous other attempts to arrive at a viable theory of quantum gravity, some examples being the lattice theory of gravity based on the Feynman Path Integral approach and Regge Calculus, dynamical triangulations,{{Harvnb|Loll|1998}} causal sets,{{Harvnb|Sorkin|2005}} twistor models{{Harvnb|Penrose|2004|loc=ch. 33 and refs therein}} or the path integral based models of quantum cosmology.{{Harvnb|Hawking|1987}}All candidate theories still have major formal and conceptual problems to overcome. They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests (and thus to decide between the candidates where their predictions vary), although there is hope for this to change as future data from cosmological observations and particle physics experiments becomes available.{{Harvnb|Ashtekar|2007}}, {{Harvnb|Schwarz|2007}}

## Current status

(file:LIGO measurement of gravitational waves.svg|thumb|Observation of gravitational waves from binary black hole merger GW150914.)General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far passed many unambiguous observational and experimental tests. However, there are strong indications the theory is incomplete.{{Harvnb|Maddox|1998|pp=52â€“59, 98â€“122}}; {{Harvnb|Penrose|2004|loc=sec. 34.1, ch. 30}} The problem of quantum gravity and the question of the reality of spacetime singularities remain open.section Quantum gravity, above Observational data that is taken as evidence for dark energy and dark matter could indicate the need for new physics.section Cosmology, above Even taken as is, general relativity is rich with possibilities for further exploration. Mathematical relativists seek to understand the nature of singularities and the fundamental properties of Einstein's equations,{{Harvnb|Friedrich|2005}} while numerical relativists run increasingly powerful computer simulations (such as those describing merging black holes).A review of the various problems and the techniques being developed to overcome them, see {{Harvnb|Lehner|2002}} In February 2016, it was announced that the existence of gravitational waves was directly detected by the Advanced LIGO team on September 14, 2015.See {{Harvnb|Bartusiak|2000}} for an account up to that year; up-to-date news can be found on the websites of major detector collaborations such as GEO 600 {{webarchive|url=https://web.archive.org/web/20070218123705weblink |date=2007-02-18 }} and LIGOFor the most recent papers on gravitational wave polarizations of inspiralling compact binaries, see {{Harvnb|Blanchet|Faye|Iyer|Sinha|2008}}, and {{Harvnb|Arun|Blanchet|Iyer|Qusailah|2008}}; for a review of work on compact binaries, see {{Harvnb|Blanchet|2006}} and {{Harvnb|Futamase|Itoh|2006}}; for a general review of experimental tests of general relativity, see {{Harvnb|Will|2006}} A century after its introduction, general relativity remains a highly active area of research.See, e.g., the electronic review journal Living Reviews in Relativity{{clear}}

{{div col|colwidth=20em}} {{div col end}}

{{Reflist|20em}}

## References

• {{Citation|last=Alpher|first=R. A.|authorlink=Ralph Asher Alpher|last2=Herman|first2=R. C.|date=1948|title=Evolution of the universe|journal=Nature|volume=162|issue=4124|pages=774â€“775|doi=10.1038/162774b0|bibcode=1948Natur.162..774A
}}
• {{Citation|last=Anderson|first=J. D.|first2=J. K.|last2=Campbell|first3=R. F.|last3=Jurgens|last4=Lau|first4=E. L.|date=1992|contribution=Recent developments in solar-system tests of general relativity|editor-last=Sato|editor-first=H.|editor2-first=T.|editor2-last=Nakamura|title=Proceedings of the Sixth Marcel GroÃŸmann Meeting on General Relativity|publisher=World Scientific|isbn=978-981-02-0950-6|pages=353â€“355
}}

}}
}}
• {{Citation|last=Arun|first=K.G.|last2=Blanchet|first2=L.|last3=Iyer|first3=B. R.|last4=Qusailah|first4=M. S. S.|year=2008|title=Inspiralling compact binaries in quasi-elliptical orbits: The complete 3PN energy flux|arxiv=0711.0302

|bibcode = 2008PhRvD..77f4035A |doi = 10.1103/PhysRevD.77.064035|journal=Physical Review D|volume=77
pages=064035}}
• {{Citation|last=Ashby|first=Neil|title=Relativity and the Global Positioning System|url=http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/GPS/Neil_Ashby_Relativity_GPS.pdf

| journal=Physics Today|volume=55|pages=41â€“47|date=2002|doi=10.1063/1.1485583
bibcode = 2002PhT....55e..41A }}
• {{Citation

|last = Ashby
|first = Neil
|title = Relativity in the Global Positioning System
|journal = Living Reviews in Relativity
|volume = 6
|issue = 1
|pages = 1
|date = 2003
|accessdate = 2007-07-06
|doi = 10.12942/lrr-2003-1
|bibcode = 2003LRR.....6....1A
|archivedate = 2007-07-04
|df =|pmc= 5253894
|pmid=28163638
}}
• {{Citation|last=Ashtekar|first=Abhay|authorlink=Abhay Ashtekar|title=New variables for classical and quantum gravity|journal=Phys. Rev. Lett.|volume=57|pages=2244â€“2247|date=1986|doi=10.1103/PhysRevLett.57.2244|pmid=10033673|issue=18|bibcode=1986PhRvL..57.2244A
}}
• {{Citation|last=Ashtekar|first=Abhay|title=New Hamiltonian formulation of general relativity|journal=Phys. Rev.|volume=D36|issue=6|pages=1587â€“1602|date=1987|doi=10.1103/PhysRevD.36.1587|bibcode = 1987PhRvD..36.1587A }}
• {{Citation|last=Ashtekar|first=Abhay|title=LOOP QUANTUM GRAVITY: FOUR RECENT ADVANCES AND A DOZEN FREQUENTLY ASKED QUESTIONS|journal=The Eleventh Marcel Grossmann Meeting - on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories â€“ Proceedings of the MG11 Meeting on General Relativity|arxiv=0705.2222|date=2007
doi = 10.1142/9789812834300_0008|isbn=978-981-283-426-3|page=126 }}
• {{Citation|last=Ashtekar|first=Abhay|first2=Badri|last2=Krishnan|date=2004|title=Isolated and Dynamical Horizons and Their Applications|journal=Living Reviews in Relativity|volume=7|issue=1|pages=10|doi=10.12942/lrr-2004-10|pmid=28163644|pmc=5253930
bibcode = 2004LRR.....7...10A }}
• {{Citation|last=Ashtekar|first=Abhay|first2=Jerzy|last2=Lewandowski|title=Background Independent Quantum Gravity: A Status Report|journal=Class. Quantum Grav.|volume=21|date=2004|issue=15|pages=R53â€“R152|doi=10.1088/0264-9381/21/15/R01|arxiv=gr-qc/0404018|bibcode = 2004CQGra..21R..53A }}
• {{Citation|last=Ashtekar|first=Abhay|first2=Anne|last2=Magnon-Ashtekar|date=1979|doi=10.1063/1.524151|title=On conserved quantities in general relativity|journal=Journal of Mathematical Physics|volume=20|issue=5|pages=793â€“800

|bibcode = 1979JMP....20..793A }}
• {{Citation|last=Auyang|first=Sunny Y.|title=How is Quantum Field Theory Possible?|publisher=Oxford University Press|date=1995|isbn=978-0-19-509345-2
}}
• {{Citation|last=Bania|first=T. M.|first2=R. T.|last2=Rood|first3=D. S.|last3=Balser|date=2002|title=The cosmological density of baryons from observations of 3He+ in the Milky Way|journal=Nature|volume=415|pages=54â€“57|doi=10.1038/415054a|pmid=11780112|issue=6867|bibcode = 2002Natur.415...54B }}
• {{Citation|last=Barack|first=Leor|first2=Curt|last2=Cutler|date=2004|title=LISA Capture Sources: Approximate Waveforms, Signal-to-Noise Ratios, and Parameter Estimation Accuracy|journal=Phys. Rev.|volume=D69|issue=8|page=082005|doi=10.1103/PhysRevD.69.082005|arxiv=gr-qc/0310125|bibcode = 2004PhRvD..69h2005B }}
• {{Citation|last=Bardeen|first=J. M.|authorlink=James M. Bardeen|last2=Carter|first2=B.|author2-link=Brandon Carter|last3=Hawking|first3=S. W.|author3-link=Stephen Hawking|date=1973|url=http://projecteuclid.org/euclid.cmp/1103858973|title=The Four Laws of Black Hole Mechanics|journal=Comm. Math. Phys.|volume=31|issue=2|pages=161â€“170|doi=10.1007/BF01645742|bibcode = 1973CMaPh..31..161B }}
• {{Citation|last=Barish|first=Barry|date=2005|editor-first=P.|editor-last=Florides|editor2-first=B.|editor2-last=Nolan|editor3-first=A.|editor3-last=Ottewil|contribution=Towards detection of gravitational waves|title=General Relativity and Gravitation. Proceedings of the 17th International Conference|publisher=World Scientific|pages=24â€“34|isbn=978-981-256-424-5|bibcode=2005grg..conf.....F
}}
• {{Citation|last=Barstow|first=M|date=2005|last2=Bond|first2=Howard E.|last3=Holberg|first3=J. B.|last4=Burleigh|first4=M. R.|last5=Hubeny|first5=I.|last6=Koester|first6=D.|title=Hubble Space Telescope Spectroscopy of the Balmer lines in Sirius B|journal=Mon. Not. R. Astron. Soc.|volume=362|issue=4|pages=1134â€“1142|doi=10.1111/j.1365-2966.2005.09359.x|arxiv=astro-ph/0506600|bibcode=2005MNRAS.362.1134B
Barstow, Bond et al.|2005}}}}
• {hide}Citation|last=Bartusiak|first= Marcia|title= Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time|isbn= 978-0-425-18620-6|publisher=Berkley|date=2000
{edih}
}}
• {{Citation|last=Beig|first=Robert|first2=Piotr T.|last2=ChruÅ›ciel|date=2006|contribution=Stationary black holes|editor-last=FranÃ§oise|editor-first=J.-P.|editor2-first=G.|editor2-last=Naber|editor3-first=T.S.|editor3-last=Tsou|title=Encyclopedia of Mathematical Physics, Volume 2|publisher=Elsevier|arxiv=gr-qc/0502041|isbn=978-0-12-512660-1|bibcode = 2005gr.qc.....2041B|page=2041 }}
• {{Citation|last=Bekenstein|first=Jacob D.|authorlink=Jacob Bekenstein|date=1973|title=Black Holes and Entropy|journal=Phys. Rev.|volume=D7|issue=8|pages=2333â€“2346|doi=10.1103/PhysRevD.7.2333|bibcode = 1973PhRvD...7.2333B }}
• {{Citation|last=Bekenstein|first=Jacob D.|date=1974|title=Generalized Second Law of Thermodynamics in Black-Hole Physics|journal=Phys. Rev.|volume=D9|issue=12|pages=3292â€“3300|doi=10.1103/PhysRevD.9.3292|bibcode = 1974PhRvD...9.3292B }}
• {{Citation|last=Belinskii|first=V. A.|first2=I. M.|last2=Khalatnikov|author2-link=Isaak Markovich Khalatnikov|first3=E. M.|last3=Lifschitz|author3-link=Evgeny Lifshitz|date=1971|title=Oscillatory approach to the singular point in relativistic cosmology|journal=Advances in Physics|volume=19|doi=10.1080/00018737000101171|issue=80|pages=525â€“573

|bibcode = 1970AdPhy..19..525B }}; original paper in Russian: {{Citation|last=Belinsky|first=V. A.|last2=Lifshits|first2=I. M.|last3=Khalatnikov|first3=E. M.|date= 1970|title=ÐšÐ¾Ð»ÐµÐ±Ð°Ñ‚ÐµÐ»ÑŒÐ½Ñ‹Ð¹ Ð ÐµÐ¶Ð¸Ð¼ ÐŸÑ€Ð¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð¸Ñ Ðš ÐžÑÐ¾Ð±Ð¾Ð¹ Ð¢Ð¾Ñ‡ÐºÐµ Ð’ Ð ÐµÐ»ÑÑ‚Ð¸Ð²Ð¸ÑÑ‚ÑÐºÐ¾Ð¹ ÐšÐ¾ÑÐ¼Ð¾Ð»Ð¾Ð³Ð¸Ð¸|journal=Uspekhi Fizicheskikh Nauk (Ð£ÑÐ¿ÐµÑ…Ð¸ Ð¤Ð¸Ð·Ð¸Ñ‡ÐµÑÐºÐ¸Ñ… ÐÐ°ÑƒÐº)
issue=11|pages=463â€“500|bibcode = 1970UsFiN.102..463B|doi=10.3367/ufnr.0102.197011d.0463}}
• {{Citation
first= C. L.|date=2003|last2=Halpern|first2=M.|last3=Hinshaw|first3=G.|last4=Jarosik|first4=N.|last5=Kogut|first5=A.|last6=Limon|first6=M.|last7=Meyer|first7=S. S.|last8=Page|first8=L.|last9=Spergel displayauthors = 8|title=First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results|journal=Astrophys. J. Suppl. Ser.|volume=148|issue=1|pages=1â€“27|doi=10.1086/377253|arxiv= astro-ph/0302207|bibcode=2003ApJS..148....1B}}
• {{Citation|last=Berger|first=Beverly K.|date=2002|title=Numerical Approaches to Spacetime Singularities|journal=Living Reviews in Relativity|volume=5|issue=1|pages=1|doi=10.12942/lrr-2002-1|pmid=28179859|pmc=5256073
bibcode = 2002LRR.....5....1B }}
• {hide}Citation|last=BergstrÃ¶m|first=Lars|first2=Ariel|last2=Goobar|date=2003|title=Cosmology and Particle Astrophysics|edition=2nd|publisher=Wiley & Sons|isbn= 978-3-540-43128-2

{edih}
• {{Citation|last=Bertotti|first=Bruno|authorlink=Bruno Bertotti|first2=Ignazio|last2=Ciufolini|first3=Peter L.|last3=Bender|date=1987|title=New test of general relativity: Measurement of de Sitter geodetic precession rate for lunar perigee|journal=Physical Review Letters|volume=58|pages=1062â€“1065|doi=10.1103/PhysRevLett.58.1062|pmid=10034329|issue=11|bibcode=1987PhRvL..58.1062B
}}
• {{Citation|last=Bertotti|first=Bruno|first2=L.|last2=Iess|first3=P.|last3=Tortora|date=2003|title=A test of general relativity using radio links with the Cassini spacecraft|journal=Nature|volume=425|pages=374â€“376|doi=10.1038/nature01997|pmid=14508481|issue=6956|bibcode = 2003Natur.425..374B }}
• {{Citation|last=Bertschinger|first=Edmund|date=1998|title=Simulations of structure formation in the universe|journal=Annu. Rev. Astron. Astrophys.|volume=36|issue=1|pages=599â€“654|doi=10.1146/annurev.astro.36.1.599|bibcode=1998ARA&A..36..599B
}}
• {{Citation|last=Birrell|first=N. D.|first2=P. C.|last2=Davies|author2-link=Paul Davies|title=Quantum Fields in Curved Space|publisher=Cambridge University Press|date=1984|isbn=978-0-521-27858-4
}}
• {{Citation|last=Blair|first=David|authorlink=David Blair (physicist)|last2=McNamara|first2=Geoff|title=Ripples on a Cosmic Sea. The Search for Gravitational Waves|date=1997|publisher=Perseus|isbn=978-0-7382-0137-5|url=https://archive.org/details/isbn_9780738201375
}}
• {{Citation|last=Blanchet|first=L.|last2=Faye|first2=G.|last3=Iyer|first3=B. R.|last4=Sinha|first4=S.|date=2008|title=The third post-Newtonian gravitational wave polarisations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits|arxiv=0802.1249

|bibcode = 2008CQGra..25p5003B |doi = 10.1088/0264-9381/25/16/165003|journal=Classical and Quantum Gravity|volume=25|issue=16|page=165003 }}
• {{Citation|last=Blanchet|first=Luc|date=2006|title=Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries|journal=Living Reviews in Relativity|volume=9|issue=1|pages=4|doi=10.12942/lrr-2006-4|pmid=28179874|pmc=5255899|bibcode = 2006LRR.....9....4B }}
• {{Citation|last=Blandford|first=R. D.|authorlink=Roger Blandford|date=1987|contribution=Astrophysical Black Holes|editor-last=Hawking|editor-first=Stephen W.|editor2-first=Werner|editor2-last=Israel|title=300 Years of Gravitation|publisher=Cambridge University Press|pages=277â€“329|isbn=978-0-521-37976-2
}}
• {{Citation|last=BÃ¶rner|first=Gerhard|date=1993|title=The Early Universe. Facts and Fiction|publisher=Springer|isbn=978-0-387-56729-7
}}
• {{Citation|last=Brandenberger|first=Robert H.|year=2008|title=Conceptual Problems of Inflationary Cosmology and a New Approach to Cosmological Structure Formation|journal=Inflationary Cosmology|arxiv=hep-th/0701111
doi = 10.1007/978-3-540-74353-8_11|series=Lecture Notes in Physics|isbn=978-3-540-74352-1|volume=738|pages=393â€“424 }}
• {{Citation|last=Brans|first= C. H.|last2=Dicke|first2= R. H.|authorlink=Carl H. Brans|authorlink2=Robert H. Dicke|date=1961|title=Mach's Principle and a Relativistic Theory of Gravitation|journal=Physical Review|volume=124|issue=3| pages=925â€“935|doi=10.1103/PhysRev.124.925|bibcode = 1961PhRv..124..925B }}
• {{Citation|last=Bridle|first=Sarah L.|first2=Ofer|last2=Lahav|first3=Jeremiah P.|last3=Ostriker|author3-link=Jeremiah P. Ostriker|first4=Paul J.|last4=Steinhardt|author4-link=Paul Steinhardt|date=2003|title=Precision Cosmology? Not Just Yet|journal=Science|volume=299|pages=1532â€“1533|doi=10.1126/science.1082158|arxiv=astro-ph/0303180|pmid=12624255|issue=5612|bibcode = 2003Sci...299.1532B }}
• {hide}Citation|last=Bruhat|first=Yvonne|contribution=The Cauchy Problem|editor-last=Witten|editor-first=Louis|title=Gravitation: An Introduction to Current Research|publisher=Wiley|date=1962|page=130|isbn=978-1-114-29166-9
{edih}
• {{Citation|last=Buchert|first=Thomas|year=2008|title=Dark Energy from Structureâ€”A Status Report|journal=General Relativity and Gravitation|volume=40|issue=2â€“3|pages=467â€“527|doi=10.1007/s10714-007-0554-8|arxiv=0707.2153|bibcode = 2008GReGr..40..467B }}
• {{Citation|last=Buras|first=R.|first2=M.|last2=Rampp|first3=H.-Th.|last3=Janka|last4=Kifonidis|first4=K.|date=2003|title=Improved Models of Stellar Core Collapse and Still no Explosions: What is Missing?|journal=Phys. Rev. Lett.|volume=90|page=241101|doi=10.1103/PhysRevLett.90.241101|arxiv=astro-ph/0303171|pmid=12857181|issue=24|bibcode=2003PhRvL..90x1101B}}
• {{Citation|last=Caldwell|first=Robert R.|title=Dark Energy|journal=Physics World|pages=37â€“42|volume=17|date=2004|doi=10.1088/2058-7058/17/5/36| issue=5
}}
• {{Citation|last=Carlip|first=Steven|title=Quantum Gravity: a Progress Report|journal=Rep. Prog. Phys.|volume=64|issue=8|date=2001|pages=885â€“942|doi=10.1088/0034-4885/64/8/301|arxiv=gr-qc/0108040|bibcode = 2001RPPh...64..885C }}
}}
• {{Citation|first=Sean M.|last=Carroll|authorlink=Sean M. Carroll|title=The Cosmological Constant|journal=Living Reviews in Relativity|volume=4|issue=1|pages=1|date=2001|doi=10.12942/lrr-2001-1|pmid=28179856|pmc=5256042
bibcode = 2001LRR.....4....1C }}
• {{Citation|last=Carter|first=Brandon|authorlink=Brandon Carter|date=1979|contribution=The general theory of the mechanical, electromagnetic and thermodynamic properties of black holes|editor1-first=S. W.|editor1-last=Hawking|editor2-first=W.|editor2-last=Israel|title= General Relativity, an Einstein Centenary Survey|pages=294â€“369 and 860â€“863|publisher= Cambridge University Press|isbn= 978-0-521-29928-2
}}
• {{Citation|title=Astrophysical evidence for the existence of black holes|first1= Annalisa|last1=Celotti|first2= John C.|last2=Miller|first3=Dennis W.|last3=Sciama|author3-link=Dennis William Sciama|journal=Class. Quantum Grav.|volume=16|issue=12A|date=1999|pages= A3â€“A21|doi=10.1088/0264-9381/16/12A/301|arxiv=astro-ph/9912186

|bibcode= 1999CQGra..16A...3C
}}
• {hide}Citation|last=Chandrasekhar|first=Subrahmanyan|authorlink=Subrahmanyan Chandrasekhar|title=The Mathematical Theory of Black Holes|date=1983|publisher=Oxford University Press|isbn=978-0-19-850370-5
{edih}
• {{citation|last1=Chandrasekhar|first1=Subrahmanyan|title=The general theory of relativity - Why 'It is probably the most beautiful of all existing theories'|date=1984|journal=Journal of Astrophysics and Astronomy|volume=5|pages=3â€“11|bibcode=1984JApA....5....3C|doi=10.1007/BF02714967
}}
• {{Citation|first1=C.|last1=Charbonnel|first2=F.|last2=Primas

|title=The Lithium Content of the Galactic Halo Stars|journal= Astronomy & Astrophysics|volume=442|date=2005|issue=3|pages= 961â€“992|doi=10.1051/0004-6361:20042491|arxiv=astro-ph/0505247|bibcode=2005A&A...442..961C
}}
• {{Citation|last1=Ciufolini|first1=Ignazio|last2=Pavlis|first2=Erricos C.|title=A confirmation of the general relativistic prediction of the Lense-Thirring effect|journal=Nature|volume=431|doi=10.1038/nature03007|pages=958â€“960|date=2004|pmid=15496915|issue=7011

|bibcode = 2004Natur.431..958C }}
• {{Citation|last1=Ciufolini|first1=Ignazio|last2=Pavlis|first2=Erricos C.|last3=Peron|first3=R.|title=Determination of frame-dragging using Earth gravity models from CHAMP and GRACE|journal=New Astron.|volume=11|issue=8|doi=10.1016/j.newast.2006.02.001|pages=527â€“550|date=2006|bibcode = 2006NewA...11..527C }}
• {{Citation|last=Coc|first=A.|last2=Vangioniâ€Flam|first2=Elisabeth|last3=Descouvemont|first3=Pierre|last4=Adahchour|first4=Abderrahim|last5=Angulo|first5=Carmen|title=Updated Big Bang Nucleosynthesis confronted to WMAP observations and to the Abundance of Light Elements|journal=Astrophysical Journal|volume=600|date= 2004|issue=2|pages=544â€“552|doi=10.1086/380121|arxiv= astro-ph/0309480|bibcode=2004ApJ...600..544C
Coc, Vangioniâ€Flam et al.|2004}}}}
• {{Citation|last1=Cutler|first1=Curt|last2=Thorne|first2=Kip S.|contribution=An overview of gravitational wave sources|date=2002|title=Proceedings of 16th International Conference on General Relativity and Gravitation (GR16)|editor1-last=Bishop|editor1-first=Nigel|editor2-last=Maharaj|editor2-first=Sunil D.|publisher=World Scientific|isbn=978-981-238-171-2|arxiv=gr-qc/0204090

|bibcode = 2002gr.qc.....4090C|page=4090 }}
• {{Citation

|first=Neal
|last=Dalal
|first2=Daniel E.
|last2=Holz
|first3=Scott A.
|last3=Hughes
|first4=Bhuvnesh
|last4=Jain
|title=Short GRB and binary black hole standard sirens as a probe of dark energy
|journal=Phys. Rev. D
|volume=74
|issue=6
|date=2006
|page=063006
|doi=10.1103/PhysRevD.74.063006
|arxiv=astro-ph/0601275
|bibcode = 2006PhRvD..74f3006D }}
• {{Citation

|first1 = Karsten
|last1 = Danzmann
|first2 = Albrecht
|last2 = RÃ¼diger
|title = LISA Technologyâ€”Concepts, Status, Prospects
|journal = Class. Quantum Grav.
|volume = 20
|issue = 10
|date = 2003
|pages = S1â€“S9
|doi = 10.1088/0264-9381/20/10/301
|bibcode = 2003CQGra..20S...1D
|archivedate = 2007-09-26
|df =
}}
• {hide}Citation|last= Dirac|first=Paul|authorlink=Paul Dirac|title=General Theory of Relativity|publisher=Princeton University Press|date=1996|isbn=978-0-691-01146-2
{edih}
• {{Citation|last=Donoghue|first=John F.|contribution=Introduction to the Effective Field Theory Description of Gravity|date=1995|arxiv=gr-qc/9512024|editor-last=Cornet|editor-first=Fernando|title=Effective Theories: Proceedings of the Advanced School, Almunecar, Spain, 26 Juneâ€“1 July 1995|isbn=978-981-02-2908-5|publisher=World Scientific|location=Singapore|bibcode = 1995gr.qc....12024D|page=12024 }}
• {{Citation|last=Duff|first=Michael|authorlink=Michael Duff (physicist)|title=M-Theory (the Theory Formerly Known as Strings)|journal=Int. J. Mod. Phys. A|volume=11|issue=32|date=1996|pages=5623â€“5641|doi=10.1142/S0217751X96002583|arxiv=hep-th/9608117|bibcode = 1996IJMPA..11.5623D }}
• {{Citation|last=Ehlers|first=JÃ¼rgen|authorlink=JÃ¼rgen Ehlers|contribution=Survey of general relativity theory|editor-last=Israel|editor-first=Werner|title=Relativity, Astrophysics and Cosmology|date=1973|publisher=D. Reidel|pages=1â€“125|isbn=978-90-277-0369-9
}}
• {{Citation|last1=Ehlers|first1=JÃ¼rgen|last2=Falco|first2=Emilio E.|last3=Schneider|first3=Peter|title=Gravitational lenses|publisher=Springer|date=1992|isbn=978-3-540-66506-9

}}
• {hide}Citation|editor-last=Ehlers|editor-first=JÃ¼rgen|editor2-last=LÃ¤mmerzahl|editor2-first=Claus|title=Special Relativityâ€”Will it Survive the Next 101 Years?|publisher=Springer|date=2006|isbn=978-3-540-34522-0

{edih}
• {{Citation|last=Ehlers|first=JÃ¼rgen|last2= Rindler|first2=Wolfgang|authorlink2=Wolfgang Rindler|title=Local and Global Light Bending in Einstein's and other Gravitational Theories|journal=General Relativity and Gravitation|volume =29|date=1997|issue=4|doi=10.1023/A:1018843001842
bibcode = 1997GReGr..29..519E }}
• {{Citation

• {{Citation|last=Einstein|first=Albert|authorlink=Albert Einstein|date=1915|title=Die Feldgleichungen der Gravitation|journal=Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin|pages=844â€“847

• {{Citation|last=Einstein|first=Albert|authorlink=Albert Einstein|title=Die Grundlage der allgemeinen RelativitÃ¤tstheorie|journal=Annalen der Physik
issue=7url=https://einsteinpapers.press.princeton.edu/vol6-doc/311|doi=10.1002/andp.19163540702|pages=769â€“822
|bibcode = 1916AnP...354..769E }} See also English translation at Einstein Papers Project
• {{Citation|last= Einstein|first=Albert|authorlink=Albert Einstein|title=Kosmologische Betrachtungen zur allgemeinen RelativitÃ¤tstheorie|date=1917|journal=Sitzungsberichte der PreuÃŸischen Akademie der Wissenschaften|page=142|url=https://einsteinpapers.press.princeton.edu/vol6-doc/568
• {{Citation|first1=George F R|last1=Ellis|authorlink=George Francis Rayner Ellis|first2=Henk|last2=Van Elst|title=Theoretical and Observational Cosmology: Cosmological models (CargÃ¨se lectures 1998)|editor-first=Marc|editor-last=LachiÃ¨ze-Rey|date=1999|pages=1â€“116|arxiv=gr-qc/9812046|bibcode = 1999ASIC..541....1E|journal=Theoretical and Observational Cosmology : Proceedings of the NATO Advanced Study Institute on Theoretical and Observational Cosmology|volume=541|doi=10.1007/978-94-011-4455-1_1|isbn=978-0-7923-5946-3 }}
• {{citation|last1=Engler|first1=Gideon|title=Einstein and the most beautiful theories in physics|journal=International Studies in the Philosophy of Science|date=2002|volume=16|issue=1|pages=27â€“37|doi=10.1080/02698590120118800
}}
• {{Citation|first1=C. W. F.|last1=Everitt|first2= S.|last2= Buchman|first3= D. B.|last3= DeBra|first4= G. M.|last4= Keiser|contribution=Gravity Probe B: Countdown to launch|title=Gyros, Clocks, and Interferometers: Testing Relativistic Gravity in Space (Lecture Notes in Physics 562)|editor-last=LÃ¤mmerzahl|editor-first= C.|editor2-last= Everitt|editor2-first= C. W. F.|editor3-first= F. W.|editor3-last= Hehl|publisher=Springer|date=2001|pages= 52â€“82|isbn=978-3-540-41236-6
}}
• {{Citation|first1=C. W. F.|last1=Everitt|first2=Bradford|last2=Parkinson|first3=Bob|last3=Kahn|date=2007|title=The Gravity Probe B experiment. Post Flight Analysisâ€”Final Report (Preface and Executive Summary)|url=http://einstein.stanford.edu/content/exec_summary/GP-B_ExecSum-scrn.pdf

| accessdate=2007-08-05|publisher=Project Report: NASA, Stanford University and Lockheed Martin
}}
• {{Citation|last=Falcke|first=Heino|last2=Melia|first2=Fulvio|last3=Agol|first3=Eric|title=Viewing the Shadow of the Black Hole at the Galactic Center|journal=Astrophysical Journal|volume=528|pages=L13â€“L16|date=2000|arxiv=astro-ph/9912263|doi=10.1086/312423|pmid=10587484|issue=1|bibcode=2000ApJ...528L..13F}}
• {{Citation|last1=Flanagan|first1=Ã‰anna Ã‰.|first2=Scott A.|last2=Hughes|title=The basics of gravitational wave theory|journal=New J. Phys.|volume= 7|issue=1|date=2005|page= 204|doi=10.1088/1367-2630/7/1/204|arxiv= gr-qc/0501041

|bibcode = 2005NJPh....7..204F }}
• {{Citation|first=JosÃ© A.|last=Font|title=Numerical Hydrodynamics in General Relativity|journal=Living Reviews in Relativity|volume=6|issue=1|pages=2|date=2003|doi=10.12942/lrr-2003-4
pmc=5256036
|pmid=28179854
}}
• {{Citation|first=JÃ¶rg|last=Frauendiener|title=Conformal Infinity|journal=Living Reviews in Relativity|volume=7|issue=1|pages=1|date=2004|doi=10.12942/lrr-2004-1
pmc=5256109
|pmid=28179863
}}
• {{Citation|last=Friedrich|first=Helmut|title=Is general relativity 'essentially understood'?|journal=Annalen der Physik|volume=15|issue=1â€“2|date=2005|pages=84â€“108|arxiv=gr-qc/0508016|doi=10.1002/andp.200510173|bibcode = 2006AnP...518...84F }}
• {{Citation|last=Futamase|first=T.|last2=Itoh|first2=Y.|date=2006|title=The Post-Newtonian Approximation for Relativistic Compact Binaries|journal=Living Reviews in Relativity|volume=10|issue=1|pages=2|doi=10.12942/lrr-2007-2|pmid=28179819|pmc=5255906|bibcode = 2007LRR....10....2F }}
• {hide}Citation|last=Gamow|first=George|authorlink=George Gamow|title=My World Line|date=1970|isbn=978-0-670-50376-6|publisher=Viking Press
{edih}
• {{Citation|last=Garfinkle|first=David|title=Of singularities and breadmaking|url=http://www.einstein-online.info/en/spotlights/singularities_bkl/index.html|journal=Einstein Online|date=2007|accessdate=2007-08-03
}}
• JOURNAL

, Robert
, Geroch
, Robert Geroch
, Partial Differential Equations of Physics
, General Relativity
, 19
, gr-qc/9602055
, 1996
, harv, 1996gere.conf...19G
,
• {hide}Citation|last=Giulini|first=Domenico|title=Special Relativity: A First Encounter|publisher=Oxford University Press|isbn=978-0-19-856746-2|date=2005
{edih}
• {{Citation|last=Giulini|first=Domenico|contribution=Algebraic and Geometric Structures in Special Relativity|editor-last=Ehlers|editor-first=JÃ¼rgen|editor2-last=LÃ¤mmerzahl|editor2-first=Claus|title=Special Relativityâ€”Will it Survive the Next 101 Years?|volume=702|date=2006|isbn=978-3-540-34522-0|pages=45â€“111|arxiv=math-ph/0602018|bibcode = 2006math.ph...2018G
series=Lecture Notes in Physics}}
• {{Citation|last=Giulini|first=Domenico|editor-last=Stamatescu|editor-first=I. O.|title=An assessment of current paradigms in the physics of fundamental interactions: Some remarks on the notions of general covariance and background independence|year=2007|isbn=978-3-540-71115-5|arxiv=gr-qc/0603087|bibcode = 2007LNP...721..105G|volume=721|pages=105â€“120|journal=Approaches to Fundamental Physics|doi=10.1007/978-3-540-71117-9_6|series=Lecture Notes in Physics }}
• {{Citation|last=Gnedin|first=Nickolay Y.|title=Digitizing the Universe|journal=Nature|volume=435|date=2005|doi=10.1038/435572a|pages=572â€“573|pmid=15931201|issue=7042|bibcode = 2005Natur.435..572G }}
• {{Citation|first=Hubert F. M.|last=Goenner|title=On the History of Unified Field Theories|journal=Living Reviews in Relativity|volume=7|issue=1|pages=2|date=2004|doi=10.12942/lrr-2004-2
pmc=5256024
|pmid=28179864
}}
• {{Citation|last=Goroff|first=Marc H.|last2=Sagnotti|first2=Augusto|title=Quantum gravity at two loops|date=1985|journal=Phys. Lett.|volume=160B|issue=1â€“3|doi=10.1016/0370-2693(85)91470-4|pages=81â€“86|bibcode = 1985PhLB..160...81G }}
• ARXIV, Eric, Gourgoulhon, 3+1 Formalism and Bases of Numerical Relativity, gr-qc/0703035, 2007, harv
,
• {{Citation|first=Robert H.|last=Gowdy|title=Gravitational Waves in Closed Universes|journal=Phys. Rev. Lett.|volume=27|issue=12|pages=826â€“829|date=1971|doi=10.1103/PhysRevLett.27.826|bibcode=1971PhRvL..27..826G
}}
• {{Citation|first=Robert H.|last=Gowdy|title=Vacuum spacetimes with two-parameter spacelike isometry groups and compact invariant hypersurfaces: Topologies and boundary conditions|journal=Annals of Physics|volume= 83|issue=1|pages=203â€“241|doi=10.1016/0003-4916(74)90384-4|date=1974|bibcode = 1974AnPhy..83..203G }}
}}
• {{Citation|last=Greenstein|first=J. L.|last2=Oke|first2=J. B.|last3=Shipman|first3=H. L.|title=Effective Temperature, Radius, and Gravitational Redshift of Sirius B|journal=Astrophysical Journal|bibcode=1971ApJ...169..563G|volume=169|page=563|date=1971|doi=10.1086/151174
}}
• {{Citation|last=Hamber|first=Herbert W.|title=Quantum Gravitation - The Feynman Path Integral Approach|publisher=Springer Publishing|date=2009|isbn=978-3-540-85292-6|doi=10.1007/978-3-540-85293-3|url=http://cds.cern.ch/record/1233211
}}
• JOURNAL, harv, GÃ¶del, Kurt, Kurt GÃ¶del, An Example of a New Type of Cosmological Solution of Einstein's Field Equations of Gravitation, Rev. Mod. Phys., 1949, 21, 447â€“450, 10.1103/RevModPhys.21.447, 3, 1949RvMP...21..447G,
• JOURNAL, Hafele, J. C., Joseph C. Hafele, Keating, R. E., Richard E. Keating, 10.1126/science.177.4044.166, Around-the-World Atomic Clocks: Predicted Relativistic Time Gains, Science (journal), Science, 177, 4044, 166â€“168, July 14, 1972, 17779917, 1972Sci...177..166H, {{harvid, Hafele, Keating, 1972a, }}
• JOURNAL, Hafele, J. C., Joseph C. Hafele, Keating, R. E., Richard E. Keating, 10.1126/science.177.4044.168, Around-the-World Atomic Clocks: Observed Relativistic Time Gains, Science (journal), Science, 177, 4044, 168â€“170, July 14, 1972, 17779918, 1972Sci...177..168H, {{harvid, Hafele, Keating, 1972b, }}
• {{Citation|last=Havas|first=P.|title=Four-Dimensional Formulation of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity|journal=Rev. Mod. Phys.|volume=36|date=1964|issue=4|pages=938â€“965|doi=10.1103/RevModPhys.36.938|bibcode=1964RvMP...36..938H}}
• {{Citation|last=Hawking|first=Stephen W.|authorlink=Stephen W. Hawking|date=1966|title=The occurrence of singularities in cosmology|journal=Proceedings of the Royal Society|volume= A294|jstor=2415489|pages=511â€“521|issue=1439|doi=10.1098/rspa.1966.0221|bibcode = 1966RSPSA.294..511H }}
• {{Citation|last=Hawking|first=S. W.|date=1975|title=Particle Creation by Black Holes|journal=Communications in Mathematical Physics|volume=43|issue=3|pages=199â€“220|doi=10.1007/BF02345020

|bibcode = 1975CMaPh..43..199H }}
• {{Citation|last=Hawking|first=Stephen W.|contribution=Quantum cosmology|pages =631â€“651|editor2-last=Israel|editor2-first=Werner|editor1-last=Hawking|editor1-first=Stephen W.|title=300 Years of Gravitation|publisher=Cambridge University Press|date=1987|isbn=978-0-521-37976-2
}}
• {{Citation|last1=Hawking|first1=Stephen W.|last2=Ellis|first2=George F. R.|author2-link=George Francis Rayner Ellis|title=The large scale structure of space-time|publisher=Cambridge University Press|isbn=978-0-521-09906-6|date=1973|title-link=The large scale structure of space-time
}}
• {{Citation|last=Heckmann|first=O. H. L.|last2=SchÃ¼cking|first2=E.|contribution=Newtonsche und Einsteinsche Kosmologie|editor-last=FlÃ¼gge|editor-first=S.|title=Encyclopedia of Physics|volume=53|page=489|date=1959
}}
• {{Citation|last=Heusler|first=Markus|title=Stationary Black Holes: Uniqueness and Beyond|journal=Living Reviews in Relativity|volume=1|issue=1|pages=6|date=1998|doi=10.12942/lrr-1998-6|pmid=28937184|pmc=5567259|bibcode = 1998LRR.....1....6H }}
• {hide}Citation|last=Heusler|first=Markus| title=Black Hole Uniqueness Theorems|publisher=Cambridge University Press|date=1996|isbn=978-0-521-56735-0
{edih}
• {{Citation|last=Hey|first=Tony|last2=Walters|first2=Patrick|title=The new quantum universe|publisher=Cambridge University Press|date=2003|isbn=978-0-521-56457-1|bibcode=2003nqu..book.....H
}}
• {{Citation|first1=Jim|last1= Hough|first2=Sheila|last2=Rowan|title=Gravitational Wave Detection by Interferometry (Ground and Space)|journal=Living Reviews in Relativity|volume=3|issue= 1|pages= 3|date=2000|bibcode=2000LRR.....3....3R|doi=10.12942/lrr-2000-3|pmid= 28179855|pmc= 5255574
}}

| doi=10.1073/pnas.15.3.168|pmid=16577160|issue=3|pmc=522427|bibcode=1929PNAS...15..168H
}}
• {{Citation|last1=Hulse|first1=Russell A.|authorlink=Russell Alan Hulse|last2=Taylor|first2=Joseph H.|author2-link=Joseph Hooton Taylor, Jr.|journal=Astrophys. J.|title=Discovery of a pulsar in a binary system|volume=195|date=1975|pages=L51â€“L55|bibcode=1975ApJ...195L..51H|doi=10.1086/181708
}}
• {{Citation|last=Ibanez|first=L. E.|title=The second string (phenomenology) revolution|journal=Class. Quantum Grav.|volume=17|issue=5|date=2000|pages=1117â€“1128|doi=10.1088/0264-9381/17/5/321|arxiv=hep-ph/9911499|bibcode = 2000CQGra..17.1117I }}
• {{Citation| last1=Iorio| first1=L.| title=An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging| journal=Space Sci. Rev.| doi=10.1007/s11214-008-9478-1| date=2009| volume=148| issue=1â€“4| pages=363â€“381
arxiv = 0809.1373 }}
• {{Citation|last=Isham|first=Christopher J.|authorlink=Christopher Isham|contribution=Prima facie questions in quantum gravity|editor-last=Ehlers|editor-first=JÃ¼rgen|editor2-last=Friedrich|editor2-first=Helmut|title=Canonical Gravity: From Classical to Quantum|date=1994|publisher=Springer|isbn=978-3-540-58339-4
}}
• {{Citation|last=Israel|first=Werner|authorlink=Werner Israel|date= 1971|title=Event Horizons and Gravitational Collapse|journal= General Relativity and Gravitation|volume= 2|issue=1|doi=10.1007/BF02450518|pages= 53â€“59|bibcode = 1971GReGr...2...53I }}
• {{Citation|last=Israel|first=Werner|contribution=Dark stars: the evolution of an idea|editor2-last=Israel|editor2-first=Werner|editor1-last=Hawking|editor1-first=Stephen W.|title=300 Years of Gravitation|publisher=Cambridge University Press|date=1987|pages=199â€“276|isbn=978-0-521-37976-2
}}
• {{Citation|last=Janssen|first=Michel|title=Of pots and holes: Einstein's bumpy road to general relativity|journal=Annalen der Physik|volume= 14|issue=S1|date=2005|pages=58â€“85|url=https://netfiles.umn.edu/xythoswfs/webui/_xy-15267453_1-t_ycAqaW0A

|format=PDF| doi=10.1002/andp.200410130|bibcode = 2005AnP...517S..58J }}
• {{Citation|first1=Piotr|last1=Jaranowski|first2=Andrzej|last2=KrÃ³lak

|title=Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case|journal=Living Reviews in Relativity|volume=8|issue=1|pages=3|date=2005|doi=10.12942/lrr-2005-3|pmid=28163647|pmc=5253919|bibcode = 2005LRR.....8....3J }}
• {{Citation|last=Kahn|first=Bob|date=1996â€“2012|title=Gravity Probe B Website|url=http://einstein.stanford.edu/|accessdate=2012-04-20|publisher=Stanford University
}}
• {{Citation|last=Kahn|first=Bob|date=April 14, 2007|url=http://einstein.stanford.edu/content/press_releases/SU/pr-aps-041807.pdf

| title=Was Einstein right? Scientists provide first public peek at Gravity Probe B results (Stanford University Press Release)|publisher=Stanford University News Service
}}
• {{Citation|last=Kamionkowski|first=Marc|first2=Arthur|last2=Kosowsky|first3=Albert|last3=Stebbins|title=Statistics of Cosmic Microwave Background Polarization|journal=Phys. Rev.|volume=D55|issue=12|date=1997|pages=7368â€“7388|doi=10.1103/PhysRevD.55.7368|arxiv=astro-ph/9611125|bibcode = 1997PhRvD..55.7368K }}
• {{Citation|last=Kennefick|first=Daniel|contribution=Astronomers Test General Relativity: Light-bending and the Solar Redshift|pages=178â€“181|editor-last=Renn|editor-first=JÃ¼rgen|title=One hundred authors for Einstein|date=2005|publisher=Wiley-VCH|isbn=978-3-527-40574-9}}
• {{Citation|last=Kennefick|first=Daniel|date=2007|contribution=Not Only Because of Theory: Dyson, Eddington and the Competing Myths of the 1919 Eclipse Expedition|title=Proceedings of the 7th Conference on the History of General Relativity, Tenerife, 2005|arxiv=0709.0685|bibcode = 2007arXiv0709.0685K|volume=0709|page=685|doi=10.1016/j.shpsa.2012.07.010}}
• {{Citation|last=Kenyon|first=I. R.|title=General Relativity|publisher=Oxford University Press|date=1990|isbn=978-0-19-851996-6
}}
• {{Citation|first=C.S.|last=Kochanek|first2=E.E.|last2=Falco|first3=C.|last3=Impey|first4=J.|last4=Lehar|title=CASTLES Survey Website|url=http://cfa-www.harvard.edu/castles|publisher=Harvard-Smithsonian Center for Astrophysics|accessdate=2007-08-21|date=2007
}}
• {{Citation|last=Komar|first=Arthur|title=Covariant Conservation Laws in General Relativity|doi=10.1103/PhysRev.113.934|journal=Phys. Rev.|volume=113|issue=3|pages=934â€“936|date=1959|bibcode = 1959PhRv..113..934K }}
• {{Citation|last=Kramer|first=Michael|pages=33â€“54|editor1-last=Karshenboim|editor1-first=S. G.|editor2-last=Peik|editor2-first=E.|title=Astrophysics, Clocks and Fundamental Constants: Millisecond Pulsars as Tools of Fundamental Physics|date=2004|arxiv=astro-ph/0405178|bibcode = 2004LNP...648...33K|volume=648|journal=Lecture Notes in Physics|doi=10.1007/978-3-540-40991-5_3|isbn=978-3-540-21967-5 }}
• {{Citation|last=Kramer|first=M.|first2=I. H.|last2=Stairs|first3=R. N.|last3=Manchester|first4=M. A.|last4=McLaughlin|last5=Lyne|date=2006|first5=A. G.|last6=Ferdman|first6=R. D.|last7=Burgay|first7=M.|last8=Lorimer|first8=D. R.|last9=Possenti
displayauthors = 8|title=Tests of general relativity from timing the double pulsar|journal=Science|volume=314|issue=5796|pages=97â€“102|arxiv=astro-ph/0609417|doi=10.1126/science.1132305bibcode = 2006Sci...314...97K }}
• {hide}Citation|last=Kraus|first=Ute|date=1998|contribution=Light Deflection Near Neutron Stars|title=Relativistic Astrophysics|publisher=Vieweg|isbn=978-3-528-06909-4|pages=66â€“81

{edih}
• {{Citation|last=KuchaÅ™|first=Karel|contribution=Canonical Quantization of Gravity|editor-last=Israel|editor-first=Werner|title=Relativity, Astrophysics and Cosmology|date=1973|publisher=D. Reidel|pages=237â€“288|isbn=978-90-277-0369-9
}}
• {{Citation|last=KÃ¼nzle|first=H. P.|title=Galilei and Lorentz Structures on spacetime: comparison of the corresponding geometry and physics|journal=Annales de l'Institut Henri PoincarÃ© A|volume=17|date=1972|pages=337â€“362|url=http://www.numdam.org/item?id=AIHPA_1972__17_4_337_0 }}
• {{Citation|last=Lahav|first=Ofer|first2=Yasushi|last2=Suto|date=2004|title=Measuring our Universe from Galaxy Redshift Surveys|journal=Living Reviews in Relativity|volume=7|issue=1|pages=8|doi=10.12942/lrr-2004-8|pmid=28163643|pmc=5253994
bibcode = 2004LRR.....7....8L }}
• {{Citation|last=Landau|first=L. D.|last2=Lifshitz|first2=E. M.|title=The Classical Theory of Fields, v. 2|date=1975|publisher=Elsevier Science, Ltd.|isbn=978-0-08-018176-9
}}
• {{Citation|last=Landgraf|first=M.|first2=M.|last2=Hechler|first3=S.|last3=Kemble|date=2005|title=Mission design for LISA Pathfinder|journal=Class. Quantum Grav.|volume=22|issue=10|pages=S487â€“S492|arxiv=gr-qc/0411071|doi=10.1088/0264-9381/22/10/048|bibcode = 2005CQGra..22S.487L }}
• {{Citation|last=Lehner|first=Luis|title=Numerical Relativity: A review|journal =Class. Quantum Grav.|volume=18|issue=17|date=2001|pages=R25â€“R86|doi=10.1088/0264-9381/18/17/202|arxiv=gr-qc/0106072|bibcode = 2001CQGra..18R..25L }}
• {{Citation|last=Lehner|first=Luis|date=2002|title=NUMERICAL RELATIVITY: STATUS AND PROSPECTS |journal=General Relativity and Gravitation: Proceedings of the 16th International Conference|arxiv=gr-qc/0202055
doi = 10.1142/9789812776556_0010|isbn=978-981-238-171-2|page=210 }}
• {{Citation|authorlink=Andrei Linde|last=Linde|first=Andrei|year=2005|title=Particle Physics and Inflationary Cosmology|journal=Contemp.concepts Phys|volume=5|pages=1â€“362|arxiv=hep-th/0503203|isbn=978-3-7186-0489-0|bibcode = 2005hep.th....3203L
}}
• {{Citation|authorlink=Andrei Linde|last=Linde|first=Andrei|year=2006|journal=J. Phys. Conf. Ser.|title=Towards inflation in string theory|volume=24|issue=1|pages=151â€“160|arxiv=hep-th/0503195|doi=10.1088/1742-6596/24/1/018|bibcode = 2005JPhCS..24..151L }}
• {{Citation|last=Loll|first=Renate|title=Discrete Approaches to Quantum Gravity in Four Dimensions|journal=Living Reviews in Relativity|volume=1|issue=1|pages=13|date=1998|doi=10.12942/lrr-1998-13|pmid=28191826|pmc=5253799
bibcode = 1998LRR.....1...13L }}
• {{Citation|last=Lovelock|first=David|title=The Four-Dimensionality of Space and the Einstein Tensor|journal=J. Math. Phys.|volume=13|date=1972|issue=6|pages=874â€“876|doi=10.1063/1.1666069

|bibcode = 1972JMP....13..874L }}
• BOOK, Ludyk, GÃ¼nter, Einstein in Matrix Form, 2013, Springer, Berlin, 978-3-642-35797-8, 1st,
• {{Citation|last=MacCallum|first=M.|contribution=Finding and using exact solutions of the Einstein equations|arxiv=gr-qc/0601102|title=AIP Conference Proceedings|type=A Century of Relativity Physics: ERE05, the XXVIII Spanish Relativity Meeting|editor-first=L.|editor-last=Mornas|editor2-first=J. D.|editor2-last=Alonso|date=2006
doi = 10.1063/1.2218172|volume=841|pages=129â€“143}}
}}
• {{Citation|last=Mannheim|first=Philip D.|date=2006|title=Alternatives to Dark Matter and Dark Energy|journal=Prog. Part. Nucl. Phys.|volume=56|issue=2|pages=340â€“445|arxiv=astro-ph/0505266|doi=10.1016/j.ppnp.2005.08.001|bibcode = 2006PrPNP..56..340M }}
• {{Citation| last=Mather|first=J. C.|first2=E. S.|last2=Cheng|first3=D. A.|last3=Cottingham|first4=R. E.|last4=Eplee|authorlink=John C. Mather| last5=Fixsen|date=1994| first5=D. J.|bibcode=1994ApJ...420..439M| last6=Hewagama| first6=T.| last7=Isaacman| first7=R. B.| last8=Jensen| first8=K. A.| last9=Meyer
displayauthors = 8|title=Measurement of the cosmic microwave spectrum by the COBE FIRAS instrument|journal=Astrophysical Journal|volume=420|pages=439â€“444|doi=10.1086/173574}}
• {{Citation|last=Mermin|first=N. David|authorlink=David Mermin|title=It's About Time. Understanding Einstein's Relativity|publisher= Princeton University Press|date=2005|isbn=978-0-691-12201-4

}}
• {hide}Citation|last=Messiah|first=Albert|title=Quantum Mechanics|publisher=Dover Publications|date=1999|isbn=978-0-486-40924-5
{edih}
• {{Citation|last=Miller|first=Cole|date=2002|url=http://www.astro.umd.edu/~miller/teaching/astr606/|title=Stellar Structure and Evolution (Lecture notes for Astronomy 606)|publisher=University of Maryland|accessdate=2007-07-25
}}
}}
• {{Citation|first=Christian|last=MÃ¸ller|title=The Theory of Relativity|publisher=Oxford University Press|date=1952|edition=3rd|url=https://archive.org/details/theoryofrelativi029229mbp|isbn=
}}
• {{Citation|last=Narayan|first=Ramesh|date=2006|doi=10.1088/1367-2630/7/1/199|title=Black holes in astrophysics|journal=New Journal of Physics|volume=7|issue=1|page=199|arxiv=gr-qc/0506078|bibcode=2005NJPh....7..199N
}}
• ARXIV, Narayan, Ramesh, Bartelmann, Matthias, Lectures on Gravitational Lensing, 1997, astro-ph/9606001, harv
,
• {{Citation

|last=Narlikar
|first=Jayant V.
|title=Introduction to Cosmology
|publisher=Cambridge University Press
|date=1993
|isbn=978-0-521-41250-6
}}
• {{Citation|last=Nieto|first=Michael Martin|title=The quest to understand the Pioneer anomaly|journal=EurophysicsNews|volume=37|date=2006|pages=30â€“34|url=http://www.europhysicsnews.org/articles/epn/pdf/2006/06/epn06604.pdf

| issue=6
bibcode = 2006ENews..37f..30N |arxiv=gr-qc/0702017}}
• {{Citation|last=NordstrÃ¶m|first=Gunnar|authorlink=Gunnar NordstrÃ¶m|date=1918|title=On the Energy of the Gravitational Field in Einstein's Theory|journal=Verhandl. Koninkl. Ned. Akad. Wetenschap.|volume=26|url=|pages=1238â€“1245|bibcode=1918KNAB...20.1238N
}}
• ARXIV, Nordtvedt, Kenneth, 2003, Lunar Laser Rangingâ€”a comprehensive probe of post-Newtonian gravity, gr-qc/0301024, harv
,
• {{Citation|first= John D.|last=Norton|title=What was Einstein's principle of equivalence?|journal= Studies in History and Philosophy of Science|date=1985|volume= 16|issue= 3|pages=203â€“246|accessdate=2007-06-11|url=http://www.pitt.edu/~jdnorton/papers/ProfE_re-set.pdf

| doi=10.1016/0039-3681(85)90002-0
}}
• {{Citation

|last=Ohanian
|first=Hans C.
|last2=Ruffini
|first2=Remo
|title=Gravitation and Spacetime
|date=1994
|publisher=W. W. Norton & Company
|isbn=978-0-393-96501-8
}}
• {{Citation|last=Olive|first=K. A.|first2=E. A.|last2=Skillman|date=2004|title=A Realistic Determination of the Error on the Primordial Helium Abundance|journal=Astrophysical Journal|volume=617|issue=1|pages=29â€“49|arxiv=astro-ph/0405588|doi=10.1086/425170|bibcode=2004ApJ...617...29O
}}
• {{Citation
first= John M.|last2=Tytler|date=2001|first2=David|last3=Kirkman|first3=David|last4=Suzuki|first4=Nao|last5=Prochaska|first5=Jason X.|last6=Lubin|first6=Dan|last7=Wolfe|first7=Arthur M.|title=The Deuterium to Hydrogen Abundance Ratio Towards a Fourth QSO: HS0105+1619|journal=Astrophysical Journal|volume=552|issue=2|pages=718â€“730|arxiv=astro-ph/0011179|doi=10.1086/320579|bibcode=2001ApJ...552..718O}}
• {{Citation|authorlink=Robert Oppenheimer|last=Oppenheimer|first=J. Robert|first2=H.|last2=Snyder|date=1939|title=On continued gravitational contraction|journal=Physical Review|volume=56|issue=5|pages=455â€“459|doi=10.1103/PhysRev.56.455|bibcode = 1939PhRv...56..455O }}
• {hide}Citation|last=Overbye|first=Dennis|authorlink=Dennis Overbye|title=Lonely Hearts of the Cosmos: the story of the scientific quest for the secret of the Universe|publisher=Back Bay|date=1999|isbn=978-0-316-64896-7
{edih}
• {{Citation|last=Pais|first=Abraham|authorlink=Abraham Pais|title='Subtle is the Lord ...' The Science and life of Albert Einstein|publisher=Oxford University Press|date=1982|isbn=978-0-19-853907-0|url=https://archive.org/details/subtleislordscie00pais
}}
• {{Citation|last=Peacock|first=John A.|date=1999|title=Cosmological Physics|publisher=Cambridge University Press|isbn=978-0-521-41072-4
}}
• {{Citation|last=Peebles|first=P. J. E.|authorlink=Jim Peebles|date=1966|title=Primordial Helium abundance and primordial fireball II|journal=Astrophysical Journal|volume=146|pages=542â€“552|bibcode=1966ApJ...146..542P|doi=10.1086/148918
}}
• {{Citation|last=Peebles|first=P. J. E.|title=Principles of physical cosmology|publisher=Princeton University Press|date=1993|isbn=978-0-691-01933-8|url=https://archive.org/details/principlesofphys00pjep
}}
• {{Citation|last=Peebles|first=P.J.E.|first2=D.N.|last2=Schramm|first3=E.L.|last3=Turner|first4=R.G.|last4=Kron|date=1991|doi=10.1038/352769a0|title=The case for the relativistic hot Big Bang cosmology|journal=Nature|volume=352|issue=6338|pages=769â€“776|bibcode = 1991Natur.352..769P }}
• {{Citation|authorlink=Roger Penrose|last=Penrose|first=Roger|date=1965|title=Gravitational collapse and spacetime singularities|journal=Physical Review Letters|volume=14|issue=3|pages=57â€“59|doi=10.1103/PhysRevLett.14.57|bibcode=1965PhRvL..14...57P}}
• {{Citation|authorlink=Roger Penrose|last=Penrose|first=Roger|date=1969|title=Gravitational collapse: the role of general relativity|journal=Rivista del Nuovo Cimento|volume=1|pages=252â€“276|bibcode = 1969NCimR...1..252P }}
}}
• {{Citation|authorlink=Arno Penzias|last=Penzias|first=A. A.|author2-link=Robert W. Wilson|first2=R. W.|last2=Wilson|date=1965|title=A measurement of excess antenna temperature at 4080 Mc/s|journal=Astrophysical Journal|volume=142|pages=419â€“421|bibcode=1965ApJ...142..419P|doi=10.1086/148307
}}
}}
• {{Citation|first=Michael E.|last=Peskin|title=Dark Matter and Particle Physics|date=2007|arxiv=0707.1536
doi = 10.1143/JPSJ.76.111017|journal=Journal of the Physical Society of Japan|volume=76|issue=11|page=111017 }}
• {{Citation|last=Poisson|first=Eric|date=2004|title=The Motion of Point Particles in Curved Spacetime|journal=Living Reviews in Relativity|volume=7|issue=1|pages=6|doi=10.12942/lrr-2004-6|pmid=28179866|pmc=5256043
bibcode = 2004LRR.....7....6P }}
• {{Citation|last=Poisson|first=Eric|date=2004|title=A Relativist's Toolkit. The Mathematics of Black-Hole Mechanics|publisher= Cambridge University Press|isbn= 978-0-521-83091-1|bibcode=2004rtmb.book.....P
}}
• {{Citation|last=Polchinski|first=Joseph|date=1998a|title=String Theory Vol. I: An Introduction to the Bosonic String|publisher=Cambridge University Press|isbn=978-0-521-63303-1|authorlink=Joseph Polchinski
}}
• {{Citation|last=Polchinski|first=Joseph|date=1998b|title=String Theory Vol. II: Superstring Theory and Beyond|publisher=Cambridge University Press|isbn=978-0-521-63304-8
}}
• {{Citation|last=Pound|first=R. V.|first2=G. A.|last2=Rebka|date=1959|doi=10.1103/PhysRevLett.3.439|title=Gravitational Red-Shift in Nuclear Resonance|journal=Physical Review Letters|volume=3|issue=9|pages= 439â€“441|bibcode=1959PhRvL...3..439P
}}
• {{Citation|last=Pound|first=R. V.|first2=G. A.|last2=Rebka|date=1960|doi=10.1103/PhysRevLett.4.337|title=Apparent weight of photons|journal=Phys. Rev. Lett.|volume=4|issue=7|pages=337â€“341|bibcode=1960PhRvL...4..337P
}}
• {{Citation|last=Pound|first=R. V.|first2=J. L.|last2=Snider|date=1964|title=Effect of Gravity on Nuclear Resonance|journal=Phys. Rev. Lett.|volume=13|issue=18|pages=539â€“540|doi=10.1103/PhysRevLett.13.539|bibcode=1964PhRvL..13..539P
}}
{edih}
• {{Citation|last=Rees|first=Martin|title=Appearance of Relativistically Expanding Radio Sources|journal=Nature|volume=211|date=1966|issue=5048|pages=468â€“470|doi=10.1038/211468a0|bibcode = 1966Natur.211..468R }}
• {{Citation

|last=Reissner
|first=H.|date=1916|title=Ãœber die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie|journal=Annalen der Physik|volume=355
|issue=9|pages=106â€“120|doi=10.1002/andp.19163550905
url=https://zenodo.org/record/1447315}}
• {{Citation|last=Remillard|first=Ronald A.|last2=Lin|first2=Dacheng|last3=Cooper|first3=Randall L.|last4=Narayan|first4=Ramesh|title=The Rates of Type I X-Ray Bursts from Transients Observed with RXTE: Evidence for Black Hole Event Horizons|journal=Astrophysical Journal|volume=646|issue=1|pages=407â€“419|date=2006|arxiv=astro-ph/0509758|doi=10.1086/504862|bibcode=2006ApJ...646..407R
}}
• {{Citation|editor-first=JÃ¼rgen|editor-last=Renn|title=The Genesis of General Relativity (4 Volumes)|place=Dordrecht|publisher=Springer|date=2007|isbn=978-1-4020-3999-7}}
• {{Citation|editor-first=JÃ¼rgen|editor-last=Renn|title=Albert Einsteinâ€”Chief Engineer of the Universe: Einstein's Life and Work in Context|place=Berlin|publisher=Wiley-VCH|date=2005|isbn=978-3-527-40571-8}}
• {{Citation

|first= Oscar A.|last=Reula|title=Hyperbolic Methods for Einstein's Equations|journal=Living Reviews in Relativity|volume=1|issue=1|pages=3|date=1998|doi= 10.12942/lrr-1998-3
pmc=5253804
|pmid=28191833
}}
• {{Citation|last=Rindler|first=Wolfgang|authorlink=Wolfgang Rindler|title=Relativity. Special, General and Cosmological|publisher=Oxford University Press|date=2001|isbn=978-0-19-850836-6
}}
• {hide}Citation|last=Rindler|first=Wolfgang|title=Introduction to Special Relativity|publisher= Clarendon Press, Oxford|date=1991|isbn=978-0-19-853952-0
{edih}
• {hide}Citation|last=Robson|first=Ian|date=1996|title=Active galactic nuclei|publisher=John Wiley|isbn=978-0-471-95853-6
{edih}
• {{Citation|last=Roulet|first=E.|first2=S.|last2=Mollerach|date=1997|title=Microlensing|journal=Physics Reports|volume=279|issue=2|pages=67â€“118|doi=10.1016/S0370-1573(96)00020-8

|arxiv = astro-ph/9603119 |bibcode = 1997PhR...279...67R }}
• {{citation|last=Rovelli|first=Carlo (ed.)|title=General Relativity: The most beautiful of theories (de Gruyter Studies in Mathematical Physics)|date=2015|publisher=Walter de Gruyter GmbH|location=Boston|isbn=978-3110340426
}}
• ARXIV, Rovelli, Carlo, Carlo Rovelli, 2000, Notes for a brief history of quantum gravity, gr-qc/0006061, harv
,
• {{Citation|last=Rovelli|first=Carlo|title=Loop Quantum Gravity|journal=Living Reviews in Relativity|volume=1|issue=1|pages=1|date=1998|doi=10.12942/lrr-1998-1|pmid=28937180|pmc=5567241|citeseerx=10.1.1.90.7036
bibcode = 1998LRR.....1....1R }}
• {{Citation|last=SchÃ¤fer|first=Gerhard|date=2004|title=Gravitomagnetic Effects|journal=General Relativity and Gravitation|volume=36|issue=10|pages=2223â€“2235|arxiv=gr-qc/0407116|doi=10.1023/B:GERG.0000046180.97877.32|bibcode = 2004GReGr..36.2223S }}
• {{Citation| last=SchÃ¶del|first=R.|first2=T.|last2=Ott|first3=R.|last3=Genzel|last4=Eckart|first4=A.
date=2003| first5=N.| last6=Alexander| first6=T.|title=Stellar Dynamics in the Central Arcsecond of Our Galaxy|journal=Astrophysical Journal|volume=596| issue=2|pages=1015â€“1034|arxiv=astro-ph/0306214|doi=10.1086/378122| bibcode=2003ApJ...596.1015S}}
• {{Citation|last=Schutz|first=Bernard F.|title=A first course in general relativity|publisher=Cambridge University Press|date=1985|isbn=978-0-521-27703-7
}}
• {{Citation|last=Schutz|first=Bernard F.|contribution=Gravitational radiation|title=Encyclopedia of Astronomy and Astrophysics|editor-last=Murdin|editor-first=Paul|publisher=Grove's Dictionaries|isbn=978-1-56159-268-5|date=2001

}}
• {{Citation|last=Schutz|first=Bernard F.|title=Gravity from the ground up|publisher=Cambridge University Press|date=2003|isbn=978-0-521-45506-0
}}
• {{Citation|last=Schwarz|first=John H.|authorlink=John H. Schwarz|title=String Theory: Progress and Problems|date=2007|arxiv=hep-th/0702219
doi = 10.1143/PTPS.170.214|journal=Progress of Theoretical Physics Supplement|volume=170|pages=214â€“226 }}
• {{Citation|last=Schwarzschild|first=Karl|authorlink=Karl Schwarzschild|title=Ãœber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie|journal=Sitzungsber. Preuss. Akad. D. Wiss.|date=1916a

|pages=189â€“196|bibcode=1916SPAW.......189S
}}
• {{Citation|last=Schwarzschild|first=Karl|authorlink=Karl Schwarzschild|title=Ãœber das Gravitationsfeld einer Kugel aus inkompressibler FlÃ¼ssigkeit nach der Einsteinschen Theorie|journal=Sitzungsber. Preuss. Akad. D. Wiss.|pages=424â€“434|date=1916b|bibcode=1916skpa.conf..424S
}}
• {{Citation|last=Seidel|first=Edward|contribution=Numerical Relativity: Towards Simulations of 3D Black Hole Coalescence|title=Gravitation and Relativity: At the turn of the millennium (Proceedings of the GR-15 Conference, held at IUCAA, Pune, India, December 16â€“21, 1997)|editor-last=Narlikar|editor-first=J. V.|editor2-last=Dadhich|editor2-first=N.|publisher=IUCAA|isbn=978-81-900378-3-9|arxiv=gr-qc/9806088|date=1998|bibcode = 1998gr.qc.....6088S|page=6088 }}
• {{Citation|last=Seljak|first=UrosÌ†|last2=Zaldarriaga|first2=Matias|title=Signature of Gravity Waves in the Polarization of the Microwave Background|journal=Phys. Rev. Lett.|volume=78|date=1997|issue=11|doi=10.1103/PhysRevLett.78.2054|arxiv=astro-ph/9609169|pages=2054â€“2057|bibcode=1997PhRvL..78.2054S
}}
• {{Citation

|last=Shapiro|first=S. S.
|last2=Davis|first2=J. L.
|last3=Lebach|first3=D. E.
|last4=Gregory|first4=J. S.|title=Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979â€“1999|journal=Phys. Rev. Lett.|volume=92|page=121101|date=2004|doi=10.1103/PhysRevLett.92.121101
|pmid=15089661
|issue=12|bibcode=2004PhRvL..92l1101S
}}
• {{Citation|authorlink=Irwin I. Shapiro|last=Shapiro|first=Irwin I.|date=1964|title=Fourth test of general relativity|journal=Phys. Rev. Lett.|volume=13|issue=26|pages=789â€“791|doi=10.1103/PhysRevLett.13.789|bibcode=1964PhRvL..13..789S
}}
first= I. I.|first2=Gordon|doi=10.1103/PhysRevLett.20.1265|last3=Ash|first3=Michael|last4=Stone|first4=Melvin|last5=Smith|first5=William|last6=Ingalls|first6=Richard|last7=Brockelman|first7=Richard|title=Fourth test of general relativity: preliminary results|journal=Phys. Rev. Lett.|volume=20|issue=22|pages=1265â€“1269|date=1968|bibcode=1968PhRvL..20.1265S}}
• {{Citation|last=Singh|first=Simon|authorlink=Simon Singh|title=Big Bang: The Origin of the Universe|publisher=Fourth Estate|date=2004|isbn=978-0-00-715251-3|title-link=Big Bang: The Origin of the Universe|bibcode=2004biba.book.....S
}}
• {{Citation|last=Sorkin|first=Rafael D.|authorlink=Rafael Sorkin|contribution=Causal Sets: Discrete Gravity|arxiv=gr-qc/0309009|editor-first=Andres|editor-last=Gomberoff|editor2-first=Donald|editor2-last=Marolf|title=Lectures on Quantum Gravity|date=2005|publisher=Springer|isbn=978-0-387-23995-8|bibcode = 2003gr.qc.....9009S|page=9009 }}
• {{Citation|last=Sorkin|first=Rafael D.|title=Forks in the Road, on the Way to Quantum Gravity|arxiv=gr-qc/9706002|journal=Int. J. Theor. Phys.|volume=36|date=1997|issue=12|doi=10.1007/BF02435709|pages=2759â€“2781|bibcode = 1997IJTP...36.2759S }}
• {{Citation| last=Spergel|first=D. N.|first2=L.|last2=Verde|first3=H. V.|last3=Peiris|first4=E.|last4=Komatsu| last5=Nolta|date=2003| first5=M. R.| last6=Bennett| first6=C. L.| last7=Halpern| first7=M.| last8=Hinshaw| first8=G.| last9=Jarosik
displayauthors = 8|title=First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters|journal=Astrophys. J. Suppl. Ser.|volume=148| issue=1|pages=175â€“194|arxiv=astro-ph/0302209|doi=10.1086/377226| bibcode=2003ApJS..148..175S}}
• {{Citation| first=D. N.|last=Spergel|first2=R.|last2=Bean|first3=O.|last3=DorÃ©|first4=M. R.| last5=Bennett|last4=Nolta| first5=C. L.| last6=Dunkley| first6=J.| last7=Hinshaw| first7=G.| last8=Jarosik| first8=N.| last9=Komatsu
displayauthors = 8|title=Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology|journal=Astrophysical Journal Supplement|volume=170| issue=2|pages=377â€“408|doi=10.1086/513700|date=2007|arxiv=astro-ph/0603449| bibcode=2007ApJS..170..377S}}
displayauthors = 8|title=Simulations of the formation, evolution and clustering of galaxies and quasars|journal=Nature|volume=435|pages=629â€“636|doi=10.1038/nature03597 issue=7042arxiv = astro-ph/0504097 }}
• {{Citation|last=Stairs|first=Ingrid H.|date=2003|title=Testing General Relativity with Pulsar Timing|journal=Living Reviews in Relativity|volume=6|issue=1|pages=5|doi=10.12942/lrr-2003-5|pmid=28163640|pmc=5253800
bibcode = 2003LRR.....6....5S }}
• {{Citation|last=Stephani|first=H.|last2=Kramer|first2=D.|last3=MacCallum|first3=M.|last4=Hoenselaers|first4=C.|last5=Herlt|first5=E.|title=Exact Solutions of Einstein's Field Equations|edition=2|publisher=Cambridge University Press|date=2003

|isbn=978-0-521-46136-8
}}
• {{Citation|last=Synge|first=J. L.|authorlink=John Lighton Synge|title=Relativity: The Special Theory|publisher=North-Holland Publishing Company|date=1972|isbn=978-0-7204-0064-9
}}
• {{Citation

|first=LÃ¡szlÃ³ B.
|title=Quasi-Local Energy-Momentum and Angular Momentum in GR
|journal=Living Reviews in Relativity
|volume=7
|issue=1
|pages=4
|date=2004
|doi=10.12942/lrr-2004-4
|pmid=28179865
|pmc=5255888
|bibcode = 2004LRR.....7....4S }}
• {{Citation|last=Taylor|first=Joseph H.|authorlink=Joseph Hooton Taylor, Jr.|date=1994|journal=Rev. Mod. Phys.|volume=66|issue=3|pages=711â€“719|title=Binary pulsars and relativistic gravity|doi=10.1103/RevModPhys.66.711|bibcode=1994RvMP...66..711T|url=http://cds.cern.ch/record/1974220
}}
• {{Citation|last=Thiemann|first=Thomas|year=2007|bibcode = 2007LNP...721..185T|ref=harv|doi=10.1007/978-3-540-71117-9_10|title=Approaches to Fundamental Physics: Loop Quantum Gravity: An Inside View|journal=Lecture Notes in Physics|isbn=978-3-540-71115-5|volume=721|pages=185â€“263|arxiv=hep-th/0608210
}}
• {{Citation|last=Thiemann|first=Thomas|title=Lectures on Loop Quantum Gravity|date=2003|journal=Lecture Notes in Physics|volume=631|pages=41â€“135|doi=10.1007/978-3-540-45230-0_3|isbn=978-3-540-40810-9|arxiv = gr-qc/0210094|bibcode=2003LNP...631...41T}}
• {{Citation|last='t Hooft|first=Gerard|last2=Veltman|first2=Martinus|date=1974|title=One Loop Divergencies in the Theory of Gravitation|journal= Ann. Inst. Poincare|volume=20|issue=1
bibcode=1974AIHPA..20...69T}}
• {{Citation|last=Thorne|first=Kip S.|authorlink=Kip Thorne|contribution=Nonspherical Gravitational Collapseâ€”A Short Review|editor-last=Klauder|editor-first=J.|title=Magic without Magic|pages=231â€“258|publisher=W. H. Freeman|date=1972
}}
• {{Citation|last=Thorne|first=Kip S.|date=1994|title=Black Holes and Time Warps: Einstein's Outrageous Legacy|publisher=W W Norton & Company|isbn=978-0-393-31276-8
}}
• {{Citation|last=Thorne|first=Kip S.|date=1995|title=Gravitational radiation|isbn=978-0-521-36853-7|arxiv= gr-qc/9506086|bibcode = 1995pnac.conf..160T|page=160|journal=Particle and Nuclear Astrophysics and Cosmology in the Next Millenium }}
• ARXIV, Townsend, Paul K., Black Holes (Lecture notes), 1997, gr-qc/9707012, harv
,
• JOURNAL, Townsend, Paul K., Four Lectures on M-Theory, High Energy Physics and Cosmology, 13, 385, 1996, hep-th/9612121, harv, 1997hepcbconf..385T
,
• {{Citation|last=Traschen|first=Jenny|title=An Introduction to Black Hole Evaporation|editor-last=Bytsenko|editor-first=A.|editor2-last=Williams|editor2-first=F.|publisher=World Scientific|date=2000|journal=Mathematical Methods of Physics (Proceedings of the 1999 Londrina Winter School)|arxiv=gr-qc/0010055|bibcode = 2000mmp..conf..180T|page=180
}}
• {{Citation|first=Andrzej|last=Trautman|contribution=Einsteinâ€“Cartan theory|title=Encyclopedia of Mathematical Physics, Vol. 2|editor-first=J.-P.|editor-last=FranÃ§oise|editor2-first=G. L.|editor2-last=Naber|editor3-last=Tsou|editor3-first=S. T.|publisher=Elsevier|date=2006|pages= 189â€“195|arxiv=gr-qc/0606062|bibcode = 2006gr.qc.....6062T }}
• {{Citation|authorlink=Bill Unruh|last=Unruh|first=W. G.|date=1976|title=Notes on Black Hole Evaporation|journal=Phys. Rev. D|volume=14|issue=4|pages=870â€“892|doi=10.1103/PhysRevD.14.870|bibcode = 1976PhRvD..14..870U }}
• {{Citation
first= M. J.|last2=Lehto|first2=H. J.|last3=Nilsson|first3=K.|last4=Heidt|first4=J.|last5=Takalo|first5=L. O.|last6=SillanpÃ¤Ã¤|first6=A.|last7=Villforth|first7=C.|last8=Kidger|first8=M.|last9=Poyner displayauthors = 8|title=A massive binary black-hole system in OJ 287 and a test of general relativity|journal=Nature|volume=452|pages=851â€“853|date=2008|doi=10.1038/nature06896|pmid=18421348|issue=7189
|bibcode = 2008Natur.452..851V |arxiv = 0809.1280 }}
• {{Citation|last=Veltman|first=Martinus|date=1975|contribution=Quantum Theory of Gravitation|title=Methods in Field Theory - Les Houches Summer School in Theoretical Physics.|editor-first=Roger|editor-last=Balian|editor2-first=Jean|editor2-last=Zinn-Justin|publisher=North Holland|volume=77}}
• {{Citation|last=Wald|first=Robert M.|authorlink=Robert M. Wald|date=1975|title=On Particle Creation by Black Holes|journal=Commun. Math. Phys.|volume=45|issue=3|pages=9â€“34|doi=10.1007/BF01609863|bibcode = 1975CMaPh..45....9W }}
• {{Citation|last=Wald|first=Robert M.|title=General Relativity|publisher=University of Chicago Press|date=1984|isbn=978-0-226-87033-5|title-link=General Relativity (book)
}}
• {{Citation|last=Wald|first=Robert M.|title=Quantum field theory in curved spacetime and black hole thermodynamics|publisher=University of Chicago Press|date=1994|isbn=978-0-226-87027-4
}}
• {{Citation|last=Wald|first=Robert M.|date=2001|title=The Thermodynamics of Black Holes|journal=Living Reviews in Relativity|volume=4|issue=1|pages=6|doi=10.12942/lrr-2001-6

|pmid=28163633|pmc=5253844
arxiv = gr-qc/9912119 }}
• {{Citation|last= Walsh|first= D.|last2=Carswell|first2=R. F.|last3=Weymann|first3=R. J.|title=0957 + 561 A, B: twin quasistellar objects or gravitational lens?|journal=Nature|volume=279|pages=381â€“4|date=1979|doi=10.1038/279381a0|pmid= 16068158|issue= 5712|bibcode=1979Natur.279..381W
}}
• {{Citation|last=Wambsganss|first=Joachim|date=1998|title=Gravitational Lensing in Astronomy|journal=Living Reviews in Relativity|volume=1|issue=1|pages=12|doi=10.12942/lrr-1998-12|pmid=28937183|pmc=5567250
bibcode = 1998LRR.....1...12W }}
• {{Citation

|last=Weinberg
|first=Steven
|title=Gravitation and Cosmology
|date=1972
|publisher=John Wiley
|isbn=978-0-471-92567-5
|url=https://archive.org/details/gravitationcosmo00stev_0
}}
• {{Citation|last=Weinberg|first=Steven|title=The Quantum Theory of Fields I: Foundations|publisher=Cambridge University Press|date=1995|isbn=978-0-521-55001-7|url=https://archive.org/details/quantumtheoryoff00stev
}}
• {hide}Citation|last=Weinberg|first=Steven|title=The Quantum Theory of Fields II: Modern Applications|publisher=Cambridge University Press|date=1996|isbn=978-0-521-55002-4
{edih}
• {hide}Citation|last=Weinberg|first=Steven|title=The Quantum Theory of Fields III: Supersymmetry|publisher=Cambridge University Press|date=2000|isbn=978-0-521-66000-6
{edih}
• {{Citation|last=Weisberg|first=Joel M.|first2=Joseph H.|last2=Taylor|author2-link=Joseph Hooton Taylor, Jr.|date=2003|contribution=The Relativistic Binary Pulsar B1913+16"|editor-last=Bailes|editor-first=M.|editor2-first=D. J.|editor2-last=Nice|editor3-first=S. E.|editor3-last=Thorsett|editor3-link=Stephen Thorsett|title=Proceedings of "Radio Pulsars," Chania, Crete, August, 2002|publisher=ASP Conference Series
}}
• {{Citation|last=Weiss|first=Achim|date=2006|url=http://www.einstein-online.info/en/spotlights/BBN_obs/index.html|title=Elements of the past: Big Bang Nucleosynthesis and observation|journal=Einstein Online|publisher=Max Planck Institute for Gravitational Physics|accessdate=2007-02-24
}}
• {{Citation|first=John A.|last=Wheeler|authorlink=John Archibald Wheeler|title=A Journey Into Gravity and Spacetime|series=Scientific American Library|place=San Francisco|isbn=978-0-7167-6034-4|publisher=W. H. Freeman|date=1990
}}
• {{Citation|last=Will|first=Clifford M.|authorlink=Clifford Will|title=Theory and experiment in gravitational physics|publisher=Cambridge University Press|date=1993|isbn=978-0-521-43973-2
}}
• {{Citation|authorlink=Clifford Will|last=Will|first=Clifford M.|date=2006|title=The Confrontation between General Relativity and Experiment|journal=Living Reviews in Relativity

|doi=10.12942/lrr-2006-3|pmid=28179873|pmc=5256066|volume=9|issue=1|pages=3
bibcode = 2006LRR.....9....3W }}
• {hide}Citation|last=Zwiebach|first=Barton|authorlink=Barton Zwiebach|title=A First Course in String Theory|publisher=Cambridge University Press|date=2004|isbn=978-0-521-83143-7
{edih}

### Popular books

• {{Citation|last=Geroch|first= R.|authorlink=Robert Geroch| title=General Relativity from A to B|location=Chicago|publisher=University of Chicago Press|date=1981|isbn=978-0-226-28864-2}}
• {{Citation|author=Lieber, Lillian|authorlink=Lillian Lieber| title=The Einstein Theory of Relativity: A Trip to the Fourth Dimension|location=Philadelphia|publisher=Paul Dry Books, Inc.|date=2008|isbn=978-1-58988-044-3}}
• BOOK, Black Holes and Time Warps: Einstein's Outrageous Legacy, Black Holes and Time Warps, Thorne, Kip, Hawking, Stephen, W. W. Norton, 1994, 0393035050, New York, Kip Thorne,
• {{Citation|author=Wald, Robert M.|authorlink=Robert Wald|title=Space, Time, and Gravity: the Theory of the Big Bang and Black Holes|location=Chicago|publisher=University of Chicago Press|date=1992|isbn=978-0-226-87029-8}}
• {{citation|authorlink=John Archibald Wheeler|last1=Wheeler|first1=John|last2=Ford|first2=Kenneth|date=1998|title=Geons, Black Holes, & Quantum Foam: a life in physics|isbn=978-0-393-31991-0|location=New York |publisher=W. W. Norton }}

• {{Citation|author=Callahan, James J.|title=The Geometry of Spacetime: an Introduction to Special and General Relativity| location=New York|publisher=Springer|date=2000|isbn=978-0-387-98641-8}}
• {{Citation|author1=Taylor, Edwin F. |author2=Wheeler, John Archibald |title=Exploring Black Holes: Introduction to General Relativity|publisher=Addison Wesley|date=2000|isbn=978-0-201-38423-9}}

• {{Citation|author=B. F. Schutz|title=A First Course in General Relativity|edition=Second|publisher=Cambridge University Press|date=2009|isbn=978-0-521-88705-2|url=https://archive.org/details/firstcourseingen00bern_0}}
• {{Citation|author=Cheng, Ta-Pei|title=Relativity, Gravitation and Cosmology: a Basic Introduction|location=Oxford and New York| publisher=Oxford University Press| date=2005|isbn=978-0-19-852957-6}}
• {{Citation|last=Gron|first=O.|last2=Hervik|first2=S.| title=Einstein's General theory of Relativity|publisher=Springer|date=2007|isbn=978-0-387-69199-2}}
• {{Citation|author=Hartle, James B.|authorlink=James Hartle|title=Gravity: an Introduction to Einstein's General Relativity|location=San Francisco|publisher=Addison-Wesley|date=2003|isbn=978-0-8053-8662-2}}
• {{Citation|author=Hughston, L. P. & Tod, K. P.|title=Introduction to General Relativity|location=Cambridge|publisher=Cambridge University Press|date=1991|isbn=978-0-521-33943-8}}
• {{Citation|author=d'Inverno, Ray|title=Introducing Einstein's Relativity|location=Oxford|publisher=Oxford University Press|date=1992|isbn=978-0-19-859686-8}}
• BOOK, Ludyk, GÃ¼nter, Einstein in Matrix Form, 2013, Springer, Berlin, 978-3-642-35797-8, First,

• {{Citation|author=Carroll, Sean M. |authorlink=Sean M. Carroll |title=Spacetime and Geometry: An Introduction to General Relativity |location=San Francisco |publisher=Addison-Wesley |date=2004 |isbn=978-0-8053-8732-2}}
• {{Citation|last=GrÃ¸n|first=Ã˜yvind |authorlink=Ã˜yvind GrÃ¸n| author2=Hervik, SigbjÃ¸rn|title=Einstein's General Theory of Relativity|location=New York|publisher=Springer|date=2007|isbn=978-0-387-69199-2}}
• {{Citation|author=Landau, Lev D.|authorlink=Lev Landau|author2= Lifshitz, Evgeny F.| author2-link=Evgeny Lifshitz|title=The Classical Theory of Fields (4th ed.)|location=London|publisher=Butterworth-Heinemann|date=1980|isbn=978-0-7506-2768-9}}
• {{Citation|author=Stephani, Hans|title=General Relativity: An Introduction to the Theory of the Gravitational Field|location=Cambridge|publisher=Cambridge University Press|date=1990|isbn=978-0-521-37941-0}}
• BOOK, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Weinberg, Steven, Wiley, 1972, 0471925675, New York, Steven Weinberg,weblink
• BOOK, Gravity: Newtonian, Post-Newtonian, Relativistic, Will, Clifford, Poisson, Eric, Cambridge University Press, 2014, 978-1107032866, Clifford M. Will,

### Specialists' books

• BOOK, The Mathematical Theory of Black Holes, Chandrasekhar, Subrahmanyan, Oxford University Press, 1983, 978-0-226-10087-6, New York, Subrahmanyan Chandrasekhar,
• BOOK, The Large Scale Structure of Space-time, The Large Scale Structure of Space-Time, Hawking, Stephen, Ellis, George, Cambridge University Press, 1975, 978-0521099066, Stephen Hawking, George F. R. Ellis,
• BOOK, A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics, Poisson, Eric, Cambridge University Press, 2007, 978-0521537803, Eric Poisson,

{{Commons category}}{{Wikiversity}}{{Wikisource portal|Relativity}}{{Wikisourcepar|Relativity: The Special and General Theory}}
{{hlist|Courses|Lectures|Tutorials}}
• {{YouTube |id=hbmf0bB38h0&list=EC6C8BDEEBA6BDC78D |title=Einstein's General Theory of Relativity}} (lecture by Leonard Susskind recorded September 22, 2008 at Stanford University).
• Series of lectures on General Relativity given in 2006 at the Institut Henri PoincarÃ© (introductory/advanced).
• WEB, Brown, Kevin, Reflections on relativity, Mathpages.com,weblink May 29, 2005,
• ARXIV, Carroll, Sean M., Lecture Notes on General Relativity, gr-qc/9712019, 1997,
• WEB, Moor, Rafi, Understanding General Relativity,weblink July 11, 2006,
• WEB, Waner, Stefan, Introduction to Differential Geometry and General Relativity,weblink 2015-04-05, PDF,
{{Relativity}}{{Theories of gravitation|PST}}{{Einstein}}{{Branches of physics}}{{Tensors}}{{Authority control}}{{Featured article}}

- content above as imported from Wikipedia
- "general relativity" does not exist on GetWiki (yet)
- time: 3:00am EDT - Thu, Aug 22 2019
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 09 JUL 2019
Eastern Philosophy
History of Philosophy
GETWIKI 09 MAY 2016
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
GETWIKI 20 AUG 2014
GETWIKI 19 AUG 2014
CONNECT