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{{General relativity sidebar}}
'''General relativity''' is a [[scientific theory|theory]] of [[gravitation]] developed by [[Albert Einstein]] between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of [[spacetime]].
By the beginning of the 20th century, [[Newton's law of universal gravitation]] had been accepted for more than two hundred years as a valid description of the gravitational force between masses. In Newton's model, gravity is the result of an attractive force between massive objects. Although even Newton was troubled by the unknown nature of that force, the basic framework was extremely successful at describing motion.
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Experiments and observations show that Einstein's description of gravitation accounts for several effects that are unexplained by Newton's law, such as minute anomalies in the [[orbit]]s of [[Mercury (planet)|Mercury]] and other [[planet]]s. General relativity also predicts novel effects of gravity, such as [[gravitational wave]]s, [[gravitational lens]]ing and an effect of gravity on time known as [[gravitational time dilation]]. Many of these predictions have been confirmed by experiment or observation, [[Gravitational wave observation|most recently gravitational waves]].
General relativity has developed into an essential tool in modern [[astrophysics]]. It provides the foundation for the current understanding of [[black hole]]s, regions of space where the gravitational effect is strong enough that even light cannot escape. Their strong gravity is thought to be responsible for the intense [[radiation]] emitted by certain types of astronomical objects (such as [[Active galactic nucleus|active galactic nuclei]] or [[
Although general relativity is not the only relativistic theory of gravity, it is the simplest one that is consistent with the experimental data. Nevertheless, a number of open questions remain, the most fundamental of which is how general relativity can be reconciled with the laws of [[Introduction to quantum mechanics|quantum physics]] to produce a complete and self-consistent theory of [[quantum gravity]].
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Several physicists, including Einstein, searched for a theory that would reconcile Newton's law of gravity and special relativity. Only Einstein's theory proved to be consistent with experiments and observations. To understand the theory's basic ideas, it is instructive to follow Einstein's thinking between 1907 and 1915, from his simple [[thought experiment]] involving an observer in free fall to his fully geometric theory of gravity.<ref>This development is traced e.g. in {{harvnb|Renn|2005|loc=p. 110ff.}}, in chapters 9 through 15 of {{harvnb|Pais|1982}}, and in {{harvnb|Janssen|2005}}. A precis of Newtonian gravity can be found in {{harvnb|Schutz|2003|loc=chapters 2–4}}. It is impossible to say whether the problem of Newtonian gravity crossed Einstein's mind before 1907, but, by his own admission, his first serious attempts to reconcile that theory with special relativity date to that year, cf. {{harvnb|Pais|1982|loc=p. 178}}.</ref>
=== Equivalence principle ===
{{main|Equivalence principle}}
A person in a [[Free fall|free-falling]] elevator experiences [[weightlessness]]; objects either float motionless or drift at constant speed. Since everything in the elevator is falling together, no gravitational effect can be observed. In this way, the experiences of an observer in free fall are indistinguishable from those of an observer in deep space, far from any significant source of gravity. Such observers are the privileged ("inertial") observers Einstein described in his theory of [[special relativity]]: observers for whom [[light]] travels along straight lines at constant speed.<ref>This is described in detail in chapter 2 of {{harvnb|Wheeler|1990}}.</ref>
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Einstein hypothesized that the similar experiences of weightless observers and inertial observers in special relativity represented a fundamental property of gravity, and he made this the cornerstone of his theory of general relativity, formalized in his [[equivalence principle]]. Roughly speaking, the principle states that a person in a free-falling elevator cannot tell that they are in free fall. Every experiment in such a free-falling environment has the same results as it would for an observer at rest or moving uniformly in deep space, far from all sources of gravity.<ref>While the equivalence principle is still part of modern expositions of general relativity, there are some differences between the modern version and Einstein's original concept, cf. {{harvnb|Norton|1985}}.</ref>
=== Gravity and acceleration ===
[[File:Elevator gravity.svg|thumb|right|236px|alt=refer to adjacent text|Ball falling to the floor in an accelerating rocket (left) and on Earth (right). The effect is identical.]]
Most effects of gravity vanish in [[free fall]], but effects that seem the same as those of gravity can be ''produced'' by an [[Acceleration|accelerated]] frame of reference. An observer in a closed room cannot tell which of the following two scenarios is true:
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An observer in an accelerated reference frame must introduce what physicists call [[fictitious force]]s to account for the acceleration experienced by the observer and objects around them. In the example of the driver being pressed into their seat, the force felt by the driver is one example; another is the force one can feel while pulling the arms up and out if attempting to spin around like a top. Einstein's master insight was that the constant, familiar pull of the Earth's gravitational field ''is fundamentally the same as these fictitious forces''.<ref>E. g. {{harvnb|Janssen|2005|loc=p. 64f}}. Einstein himself also explains this in section XX of his non-technical book Einstein 1961. Following earlier ideas by [[Ernst Mach]], Einstein also explored [[centrifugal forces]] and their gravitational analogue, cf. {{harvnb|Stachel|1989}}.</ref> The apparent magnitude of the fictitious forces always appears to be proportional to the mass of any object on which they act{{snd}}for instance, the driver's seat exerts just enough force to accelerate the driver at the same rate as the car. By analogy, Einstein proposed that an object in a gravitational field should feel a gravitational force proportional to its mass, as embodied in [[Newton's law of gravitation]].<ref>Einstein explained this in section XX of Einstein 1961. He considered an object "suspended" by a rope from the ceiling of a room aboard an accelerating rocket: from inside the room it looks as if gravitation is pulling the object down with a force proportional to its mass, but from outside the rocket it looks as if the rope is simply transferring the acceleration of the rocket to the object, and must therefore exert just the "force" to do so.</ref>
=== Physical consequences ===
In 1907, Einstein was still eight years away from completing the general theory of relativity. Nonetheless, he was able to make a number of novel, testable predictions that were based on his starting point for developing his new theory: the equivalence principle.<ref>More specifically, Einstein's calculations, which are described in chapter 11b of {{harvnb|Pais|1982}}, use the equivalence principle, the equivalence of gravity and inertial forces, and the results of special relativity for the propagation of light and for accelerated observers (the latter by considering, at each moment, the instantaneous [[inertial frame of reference]] associated with such an accelerated observer).</ref>
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In a similar way, Einstein predicted the [[Tests of general relativity#Deflection of light by the Sun|gravitational deflection of light]]: in a gravitational field, light is deflected downward, to the center of the gravitational field. Quantitatively, his results were off by a factor of two; the correct derivation requires a more complete formulation of the theory of general relativity, not just the equivalence principle.<ref>Cf. {{harvnb|Ehlers|Rindler|1997}}; for a non-technical presentation, see {{harvnb|Pössel|2007}}.</ref>
=== Tidal effects ===
[[File:Tide fall.png|thumb|150px|Two bodies falling towards the center of the Earth accelerate towards each other as they fall.]]
The equivalence between gravitational and inertial effects does not constitute a complete theory of gravity. When it comes to explaining gravity near our own ___location on the Earth's surface, noting that our reference frame is not in free fall, so that [[fictitious force]]s are to be expected, provides a suitable explanation. But a freely falling reference frame on one side of the Earth cannot explain why the people on the opposite side of the Earth experience a gravitational pull in the opposite direction.
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The equivalence between inertia and gravity cannot explain tidal effects – it cannot explain variations in the gravitational field.<ref>These and other tidal effects are described in {{harvnb|Wheeler|1990|pp=83–91}}.</ref> For that, a theory is needed which describes the way that matter (such as the large mass of the Earth) affects the inertial environment around it.
=== From acceleration to geometry ===
While Einstein was exploring the equivalence of gravity and acceleration as well as the role of tidal forces, he discovered several analogies with the [[geometry]] of [[surface (mathematics)|surfaces]]. An example is the transition from an inertial reference frame (in which free particles coast along straight paths at constant speeds) to a rotating reference frame (in which [[fictitious force]]s have to be introduced in order to explain particle motion): this is analogous to the transition from a [[Cartesian coordinate system]] (in which the coordinate lines are straight lines) to a [[Curvilinear coordinates|curved coordinate system]] (where coordinate lines need not be straight).
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After he had realized the validity of this geometric analogy, it took Einstein a further three years to find the missing cornerstone of his theory: the equations describing how [[matter]] influences spacetime's curvature. Having formulated what are now known as [[Einstein's equations]] (or, more precisely, his field equations of gravity), he presented his new theory of gravity at several sessions of the [[Prussian Academy of Sciences]] in late 1915, culminating in his final presentation on November 25, 1915.<ref>Einstein's struggle to find the correct field equations is traced in chapters 13–15 of {{harvnb|Pais|1982}}.</ref>
== Geometry and gravitation ==
Paraphrasing [[John Archibald Wheeler|John Wheeler]], Einstein's geometric theory of gravity can be summarized as: ''spacetime tells matter how to move; matter tells spacetime how to curve''.<ref>E.g. p. xi in {{harvnb|Wheeler|1990}}.</ref> What this means is addressed in the following three sections, which explore the motion of so-called [[test particle]]s, examine which properties of matter serve as a source for gravity, and, finally, introduce Einstein's equations, which relate these matter properties to the curvature of spacetime.
=== Probing the gravitational field ===
[[File:Earth geo.png|thumb|right|236px|Converging geodesics: two lines of longitude (green) that start out in parallel at the equator (red) but converge to meet at the pole]]
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Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. A chair someone is sitting on applies an external upwards force preventing the person from [[freefall|falling freely]] towards [[Travel to the Earth's center|the center of the Earth]] and thus following a geodesic, which they would otherwise be doing without the chair there, or any other matter in between them and the center point of the Earth. In this way, general relativity explains the daily experience of gravity on the surface of the Earth ''not'' as the downwards pull of a gravitational force, but as the upwards push of external forces. These forces deflect all bodies resting on the Earth's surface from the geodesics they would otherwise follow.<ref>See chapter 10 of {{harvnb|Wheeler|1990}}.</ref> For objects massive enough that their own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.<ref>In fact, when starting from the complete theory, Einstein's equation can be used to derive these more complicated laws of motion for matter as a consequence of geometry, but deriving from this the motion of idealized test particles is a highly non-trivial task, cf. {{harvnb|Poisson|2004}}.</ref>
=== Sources of gravity ===
In [[Law of universal gravitation|Newton's description of gravity]], the gravitational force is caused by matter. More precisely, it is caused by a specific property of material objects: their [[mass]]. In Einstein's theory and related [[theories of gravitation]], curvature at every point in spacetime is also caused by whatever matter is present. Here, too, mass is a key property in determining the gravitational influence of matter. But in a relativistic theory of gravity, mass cannot be the only source of gravity. Relativity links mass with energy, and energy with momentum.
The equivalence between mass and [[energy]], as expressed by the formula [[Mass–energy equivalence|''E'' = ''mc''{{smallsup|2}}]], is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity. If a physical system has energy, it also has the corresponding mass, and vice versa. In particular, all properties of a body that are associated with energy, such as its [[temperature]] or the [[binding energy]] of systems such as [[Atomic nucleus|nuclei]] or [[molecule]]s, contribute to that body's mass, and hence act as sources of gravity.<ref>A simple explanation of mass–energy equivalence can be found in sections 3.8 and 3.9 of {{harvnb|Giulini|2005}}.</ref>
In special relativity, energy is closely connected to [[momentum]]. In special relativity, just as space and time are different aspects of a more comprehensive entity called spacetime, energy and momentum are merely different aspects of a unified, four-dimensional quantity that physicists call [[four-momentum]]. In consequence, if energy is a source of gravity, momentum must be a source as well. The same is true for quantities that are directly related to energy and momentum, namely internal [[pressure]] and [[Tension (physics)|tension]]. Taken together, in general relativity it is mass, energy, momentum, pressure and tension that serve as sources of gravity: they are how matter tells spacetime how to curve. In the theory's mathematical formulation, all these quantities are but aspects of a more general physical quantity called the [[
=== Einstein's equations ===
[[Einstein's equations]] are the centerpiece of general relativity. They provide a precise formulation of the relationship between spacetime geometry and the properties of matter, using the language of mathematics. More concretely, they are formulated using the concepts of [[Riemannian geometry]], in which the geometric properties of a space (or a spacetime) are described by a quantity called a [[Metric tensor|metric]]. The metric encodes the information needed to compute the fundamental geometric notions of distance and angle in a curved space (or spacetime).
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A spherical surface like that of the Earth provides a simple example. The ___location of any point on the surface can be described by two coordinates: the geographic [[latitude]] and [[longitude]]. Unlike the Cartesian coordinates of the plane, coordinate differences are not the same as distances on the surface, as shown in the diagram on the right: for someone at the equator, moving 30 degrees of longitude westward (magenta line) corresponds to a distance of roughly {{convert|3300|km|mi|sp=us}}, while for someone at a latitude of 55 degrees, moving 30 degrees of longitude westward (blue line) covers a distance of merely {{convert|1900|km|mi|sp=us}}. Coordinates therefore do not provide enough information to describe the geometry of a spherical surface, or indeed the geometry of any more complicated space or spacetime. That information is precisely what is encoded in the metric, which is a function defined at each point of the surface (or space, or spacetime) and relates coordinate differences to differences in distance. All other quantities that are of interest in geometry, such as the length of any given curve, or the angle at which two curves meet, can be computed from this metric function.<ref>For a more detailed definition of the metric, but one that is more informal than a textbook presentation, see chapter 14.4 of {{harvnb|Penrose|2004}}.</ref>
The metric function and its rate of change from point to point can be used to define a geometrical quantity called the [[Riemann curvature tensor]], which describes exactly how the [[Riemannian manifold]], the spacetime in the theory of relativity, is curved at each point. As has already been mentioned, the matter content of the spacetime defines another quantity, the [[
: <math>\mathbf{G}=\frac{8\pi G}{c^4}\mathbf{T},</math>
i.e., up to a constant multiple, the quantity '''G''' (which measures curvature) is equated with the quantity '''T''' (which measures matter content). Here, ''G'' is the [[gravitational constant]] of Newtonian gravity, and ''c'' is the [[speed of light]] from special relativity.
This equation is often referred to in the plural as ''Einstein's equations'', since the quantities '''G''' and '''T''' are each determined by several functions of the coordinates of spacetime, and the equations equate each of these component functions.<ref>The geometrical meaning of Einstein's equations is explored in chapters 7 and 8 of {{harvnb|Wheeler|1990}}; cf. box 2.6 in {{harvnb|Thorne|1994}}. An introduction using only very simple mathematics is given in chapter 19 of {{harvnb|Schutz|2003}}.</ref> [[Exact solutions of Einstein's field equations|A solution of these equations]] describes a particular geometry of [[spacetime]]; for example, the [[Schwarzschild metric|Schwarzschild solution]] describes the geometry around a spherical, non-rotating mass such as a [[star]] or a [[black hole]], whereas the [[Kerr metric|Kerr solution]] describes a rotating black hole. Still other solutions can describe a [[gravitational wave]] or, in the case of the [[Friedmann–Lemaître–Robertson–Walker metric|Friedmann–Lemaître–Robertson–Walker solution]], an expanding universe. The simplest solution is the uncurved [[Minkowski spacetime]], the spacetime described by special relativity.<ref>The most important solutions are listed in every [[General relativity#Further reading|textbook on general relativity]]; for a (technical) summary of our current understanding, see {{harvnb|Friedrich|2005}}.</ref>
== Experiments ==
No scientific theory is self-evidently true; each is a model that must be checked by experiment. [[Newton's law of gravity]] was accepted because it accounted for the motion of planets and moons in the [[Solar System]] with considerable accuracy. As the precision of experimental measurements gradually improved, some discrepancies with Newton's predictions were observed, and these were accounted for in the general theory of relativity. Similarly, the predictions of general relativity must also be checked with experiment, and Einstein himself devised three tests now known as the classical tests of the theory:
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A number of other tests have probed the validity of various versions of the [[equivalence principle]]; strictly speaking, all measurements of gravitational time dilation are tests of the [[Weak equivalence principle|weak version of that principle]], not of general relativity itself. So far, general relativity has passed all observational tests.<ref>An accessible introduction to tests of general relativity is {{harvnb|Will|1993}}; a more technical, up-to-date account is {{harvnb|Will|2006}}.</ref>
== Astrophysical applications ==
Models based on general relativity play an important role in [[astrophysics]]; the success of these models is further testament to the theory's validity.
=== Gravitational lensing ===
[[File:Einstein cross.jpg|thumb|220px|The [[Einstein Cross]]: four images of the same distant [[quasar]], produced by a [[gravitational lens]] (the much closer foreground galaxy [[Huchra's lens]])]]
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[[Observational astronomy]] uses lensing effects as an important tool to infer properties of the lensing object. Even in cases where that object is not directly visible, the shape of a lensed image provides information about the [[mass]] distribution responsible for the light deflection. In particular, gravitational lensing provides one way to measure the distribution of [[dark matter]], which does not give off light and can be observed only by its gravitational effects. One particularly interesting application are large-scale observations, where the lensing masses are spread out over a significant fraction of the observable universe, and can be used to obtain information about the large-scale properties and evolution of our cosmos.<ref>Introductions to gravitational lensing and its applications can be found on the webpages {{harvnb|Newbury|1997}} and {{harvnb|Lochner|2007}}.</ref>
=== Gravitational waves ===
[[Gravitational wave]]s, a direct consequence of Einstein's theory, are distortions of geometry that propagate at the speed of light, and can be thought of as ripples in spacetime. They should not be confused with the [[gravity wave]]s of [[fluid dynamics]], which are a different concept.
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Currently, a number of land-based [[gravitational wave detector]]s are in operation, and a mission to launch a space-based detector, [[Laser Interferometer Space Antenna|LISA]], is currently under development, with a precursor mission ([[LISA Pathfinder]]) which was launched in 2015. Gravitational wave observations can be used to obtain information about compact objects such as neutron stars and black holes, and also to probe the state of the early [[universe]] fractions of a second after the [[Big Bang]].<ref>The ongoing search for gravitational waves is described in {{harvnb|Bartusiak|2000}} and in {{harvnb|Blair|McNamara|1997}}.</ref>
=== Black holes ===
[[File:M87 jet.jpg|thumb|right|200px|Black hole-powered jet emanating from the central region of the galaxy [[Messier 87|M87]]]]
When mass is concentrated into a sufficiently [[Hoop conjecture|compact]] region of space, general relativity predicts the formation of a [[black hole]] – a region of space with a gravitational effect so strong that not even light can escape. Certain types of black holes are thought to be the final state in the [[Stellar evolution|evolution]] of massive [[star]]s. On the other hand, [[supermassive black hole]]s with the mass of [[million]]s or [[1000000000 (number)|billions]] of [[Sun]]s are assumed to reside in the cores of most [[galaxy|galaxies]], and they play a key role in current models of how galaxies have formed over the past billions of years.<ref>For an overview of the history of black hole physics from its beginnings in the early 20th century to modern times, see the very readable account by {{harvnb|Thorne|1994}}. For an up-to-date account of the role of black holes in structure formation, see {{harvnb|Springel|White|Jenkins|Frenk|2005}}; a brief summary can be found in the related article {{harvnb|Gnedin|2005}}.</ref>
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There are several properties that make black holes the most promising sources of gravitational waves. One reason is that black holes are the most compact objects that can orbit each other as part of a binary system; as a result, the gravitational waves emitted by such a system are especially strong. Another reason follows from what are called [[No-hair theorem|black-hole uniqueness theorems]]: over time, black holes retain only a minimal set of distinguishing features (these theorems have become known as "no-hair" theorems), regardless of the starting geometric shape. For instance, in the long term, the collapse of a hypothetical matter cube will not result in a cube-shaped black hole. Instead, the resulting black hole will be indistinguishable from a black hole formed by the collapse of a spherical mass. In its transition to a spherical shape, the black hole formed by the collapse of a more complicated shape will emit gravitational waves.<ref>An elementary introduction to the black hole uniqueness theorems can be found in {{harvnb|Chrusciel|2006}} and in {{harvnb|Thorne|1994|loc=pp. 272–286}}.</ref>
=== Cosmology ===
[[File:WMAP image of the CMB anisotropy.jpg|thumb|236px|An image, created using data from the [[WMAP]] satellite telescope, of the [[radiation]] emitted no more than a few hundred thousand years after the Big Bang]]
One of the most important aspects of general relativity is that it can be applied to the [[universe]] as a whole. A key point is that, on large scales, our universe appears to be constructed along very simple lines: all current observations suggest that, on average, the structure of the cosmos should be approximately the same, regardless of an observer's ___location or direction of observation: the universe is approximately [[Homogeneity (physics)|homogeneous]] and [[isotropic]]. Such comparatively simple universes can be described by simple solutions of Einstein's equations. The current [[Physical cosmology|cosmological models]] of the universe are obtained by combining these simple solutions to general relativity with theories describing the properties of the universe's [[matter]] content, namely [[thermodynamics]], [[Nuclear physics|nuclear-]] and [[particle physics]]. According to these models, our present universe emerged from an extremely dense high-temperature state – the [[Big Bang]] – roughly 14 [[1000000000 (number)|billion]] [[year]]s ago and has been [[Cosmic expansion|expanding]] ever since.<ref>Detailed information can be found in Ned Wright's Cosmology Tutorial and FAQ, {{harvnb|Wright|2007}}; a very readable introduction is {{harvnb|Hogan|1999}}. Using undergraduate mathematics but avoiding the advanced mathematical tools of general relativity, {{harvnb|Berry|1989}} provides a more thorough presentation.</ref>
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Einstein's equations can be generalized by adding a term called the [[cosmological constant]]. When this term is present, [[Vacuum|empty space]] itself acts as a source of attractive (or, less commonly, repulsive) gravity. Einstein originally introduced this term in his pioneering 1917 paper on cosmology, with a very specific motivation: contemporary cosmological thought held the universe to be static, and the additional term was required for constructing static model universes within the framework of general relativity. When it became apparent that the universe is not static, but expanding, Einstein was quick to discard this additional term. Since the end of the 1990s, however, astronomical evidence indicating an [[Acceleration|accelerating]] expansion consistent with a cosmological constant – or, equivalently, with a particular and ubiquitous kind of [[dark energy]] – has steadily been accumulating.<ref>Einstein's original paper is {{harvnb|Einstein|1917}}; good descriptions of more modern developments can be found in {{harvnb|Cowen|2001}} and {{harvnb|Caldwell|2004}}.</ref>
== Modern research ==
General relativity is very successful in providing a framework for accurate models which describe an impressive array of physical phenomena. On the other hand, there are many interesting open questions, and in particular, the theory as a whole is almost certainly incomplete.<ref>Cf. {{harvnb|Maddox|1998|loc=pp. 52–59 and 98–122}}; {{harvnb|Penrose|2004|loc=section 34.1 and chapter 30}}.</ref>
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More than one hundred years after the theory was first published, research is more active than ever.<ref>A good starting point for a snapshot of present-day research in relativity is the electronic review journal [http://relativity.livingreviews.org Living Reviews in Relativity].</ref>
== See also ==
{{cols}}
* [[General relativity]]
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* [[General relativity#Further reading|List of books on general relativity]]{{colend}}
== References ==
{{reflist|colwidth=30em}}
== Bibliography ==
{{
* {{
| 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
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| bibcode=2002PhT....55e..41A
}}
* {{
|last = Ashby |first = Neil
|title = Relativity in the Global Positioning System
|url = http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html
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|pmc = 5253894
}}
* {{
| last=Bartusiak | first= Marcia
| title= Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time
| isbn= 978-0-425-18620-6
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| year=2000
}}
* {{
| last=Berry | first=Michael V.
| title=Principles of Cosmology and Gravitation
| publisher=Institute of Physics Publishing
| edition=1989 reprinted
| year=1989
| bibcode=1989pcg..book.....B
| isbn=0-85274-037-9
}}
* {{
| last=Bertotti | first=Bruno | author-link=Bruno Bertotti
| pages=402–405
| contribution=The Cassini Experiment: Investigating the Nature of Gravity
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| isbn=3-527-40574-7
}}
* {{
| last1=Blair | first1=David | author-link=David Blair (physicist)
| last2=McNamara | first2=Geoff
| title=Ripples on a Cosmic Sea. The Search for Gravitational Waves
| year=1997
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| url=https://archive.org/details/isbn_9780738201375
}}
* {{
| last=Caldwell | first=Robert R.
| title=Dark Energy
| journal=Physics World
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| doi=10.1088/2058-7058/17/5/36
}}
* {{
|last = Chrusciel |first = Piotr
|title = How many different kinds of black hole are there?
|year = 2006
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|archive-date = 2011-04-14
}}
* {{
| last=Cowen | first=Ron
| title=A Dark Force in the Universe
| journal=Science News
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| issue=14
| jstor=3981642}}
* {{
| last=Disney | first=Michael
| title=A New Look at Quasars
| journal=Scientific American
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| doi=10.1038/scientificamerican0698-52
| issue=6
* {{
| last1=Ehlers | first1 = Jürgen
| last2= Rindler | first2=Wolfgang | author-link2=Wolfgang Rindler
| title=Local and Global Light Bending in Einstein's and other Gravitational Theories
| journal=General Relativity and Gravitation
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| hdl-access=free
}}
* {{
| last= Einstein | first=Albert | author-link=Albert Einstein
| title=Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie
| year=1917
| journal=Sitzungsberichte der Preußischen Akademie der Wissenschaften
| page=142
| bibcode=1917SPAW.......142E
}}
* {{
| last=Einstein | first=Albert | author-link=Albert Einstein
| title=Relativity. The special and general theory
| year=1961
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| url=https://www.gutenberg.org/ebooks/5001
}}
* {{
| last=Friedrich | first=Helmut
| title=Is general relativity 'essentially understood'?
| journal=Annalen der Physik
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|bibcode = 2006AnP...518...84F | s2cid=37236624
}}
* {{
| last=Geroch | first=Robert
| title= General relativity from A to B
| publisher=University of Chicago Press
| year=1978
| isbn=0-226-28864-1 }}
* {{
| last=Giulini | first=Domenico
| title=Special relativity. A first encounter
| publisher=Oxford University Press
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| isbn=0-19-856746-4
}}
* {{
| last=Gnedin | first=Nickolay Y.
| title=Digitizing the Universe
| journal=Nature
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| year=2005
| pages=572–573
| doi=10.1038/435572a | doi-access=free
| pmid=15931201
| issue=7042
| bibcode = 2005Natur.435..572G | s2cid=3023436
}}
* {{
| last=Greene | first=Brian | author-link=Brian Greene
| title=The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
| publisher=Vintage
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| url=https://archive.org/details/elegantuniverses0000gree
}}
* {{
| last=Greene | first=Brian | author-link=Brian Greene
| title=The Fabric of the Cosmos: Space, Time, and the Texture of Reality
| publisher=A. A. Knopf
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| title-link=The Fabric of the Cosmos: Space, Time, and the Texture of Reality
}}
* {{
| last = Harrison | first = David M.
| year = 2002
| title = A Non-mathematical Proof of Gravitational Time Dilation
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| access-date = 2007-05-06
}}
* {{
| last=Hartl | first=Gerhard
| contribution=The Confirmation of the General Theory of Relativity by the British Eclipse Expedition of 1919
| pages=182–187
| editor-last=Renn | editor-first=Jürgen
| title=One hundred authors for Einstein
| year=2005
| publisher = Wiley-VCH
| isbn=3-527-40574-7 }}
* {{
| last=Hogan | first=Craig J.
| title=The Little Book of the Big Bang. A Cosmic Primer
| publisher=Springer
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| url=https://archive.org/details/littlebookofbigb0000hoga
}}
* {{
| last = Janssen | first = Michel
| title = Of pots and holes: Einstein's bumpy road to general relativity
| journal = Annalen der Physik
Line 451 ⟶ 417:
| archive-url = https://web.archive.org/web/20170713055330/https://netfiles.umn.edu/users/janss011/home%20page/potsandholes.pdf
}}
* {{
| last=Kennefick | first=Daniel
| contribution=Astronomers Test General Relativity: Light-bending and the Solar Redshift
| pages=178–181
Line 462 ⟶ 427:
| publisher = Wiley-VCH
| isbn=3-527-40574-7 }}
* {{
| last=Kennefick | first=Daniel
| year=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
| s2cid=119203172
}}
* {{
| last=Kramer | first=Michael
| contribution=Millisecond Pulsars as Tools of Fundamental Physics
| pages=33–54
Line 489 ⟶ 452:
| editor2-first=E.
| arxiv=astro-ph/0405178
| isbn=978-3-540-21967-5
}}
* {{
| last=Lehner | first=Luis
| contribution=Numerical Relativity: Status and Prospects
| arxiv=gr-qc/0202055
Line 502 ⟶ 464:
| s2cid=9145148
}}
* {{
|editor-last = Lochner |editor-first = Jim
|title = Gravitational Lensing
|journal = Imagine the Universe Website
Line 514 ⟶ 475:
|archive-date = 2007-06-17
}}
* {{
| last=Maddox | first=John | author-link=John Maddox
| title=What Remains To Be Discovered
| publisher=Macmillan
Line 524 ⟶ 483:
| url=https://archive.org/details/whatremainstobed00madd
}}
* {{
| first=N. David | last=Mermin | author-link=David Mermin
| year=2005
| title=It's About Time. Understanding Einstein's Relativity
| publisher=Princeton University Press
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| isbn=0-691-12201-6
| url-access=registration
| url=https://archive.org/details/itsabouttimeunde0000merm
}}
* {{
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| title=Does dark matter really exist?
| journal=Scientific American
Line 552 ⟶ 509:
| archive-date=2011-06-10
}}
* {{
| last=Norton | first=John D.
| title=What was Einstein's principle of equivalence?
| journal=Studies in History and Philosophy of Science
Line 566 ⟶ 522:
| bibcode=1985SHPSA..16..203N
}}
* {{
|last = Newbury |first = Pete
|title = Gravitational lensing webpages
|url = http://www.iam.ubc.ca/old_pages/newbury/lenses/research.html
Line 576 ⟶ 531:
|archive-date = 2012-12-06
}}
* {{
|last = Nieto |first = Michael Martin
|title = The quest to understand the Pioneer anomaly
|journal = Europhysics News
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|s2cid = 118949889
}}
* {{
| last = Pais | first = Abraham | author-link = Abraham Pais
| title = 'Subtle is the Lord ...' The Science and life of Albert Einstein
| publisher = Oxford University Press
Line 603 ⟶ 555:
| url = https://archive.org/details/subtleislordscie00pais
}}
* {{
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| title=The Road to Reality
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| url=https://archive.org/details/roadtorealitycom00penr_0
}}
* {{
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| year = 2007
| title = The equivalence principle and the deflection of light
Line 625 ⟶ 574:
| archive-date = 2007-05-03
}}
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| pmid=28179866
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* {{
| editor-first = Jürgen | editor-last = Renn
| title = Albert Einstein – Chief Engineer of the Universe: Einstein's Life and Work in Context
| place = Berlin| publisher = Wiley-VCH | year = 2005| isbn = 3-527-40571-2 }}
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}}
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}}
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| title=Three Roads to Quantum Gravity
| year=2001
Line 667 ⟶ 612:
| publisher=Basic | title-link=Three Roads to Quantum Gravity
}}
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}}
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| last2=White | first2=Simon D. M.
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| last11=Peacock | first11=John A.
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| title=Simulations of the formation, evolution and clustering of galaxies and quasars
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| hdl=2027.42/62586
| s2cid=4383030
}}
* {{
| last= Stachel | first=John | author-link=John Stachel
| contribution= The Rigidly Rotating Disk as the 'Missing Link in the History of General Relativity'
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| series=Einstein Studies |volume=1
Line 743 ⟶ 665:
| year=1989
| pages=48–62 }}
* {{
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| title = Black Holes and Time Warps: Einstein's Outrageous Legacy
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}}
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| title = A Journey Into Gravity and Spacetime
| series = Scientific American Library
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| publisher = W. H. Freeman
| year = 1990}}
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| issue=1
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| doi=10.12942/lrr-2006-3 | doi-access=free
| pmid=28179873 | pmc=5256066
| arxiv = gr-qc/0510072 |bibcode = 2006LRR.....9....3W | page=3
}}
* {{
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| title=Cosmology tutorial and FAQ
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Line 809 ⟶ 720:
{{Refend}}
== External links ==
{{Wikibooks|General relativity}}
{{commons category|General relativity}}
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