General relativity   Key topics  Introduction to... Mathematical formulation of...  Fundamental concepts  Special relativity Equivalence principle World line · Riemannian geometry  Phenomena  Kepler problem · Lenses · Waves Framedragging · Geodetic effect Event horizon · Singularity Black hole An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ...
Newtonâ€™s conception and quantification of gravitation held until the beginning of the 20th century, when Albert Einstein extended the special relativity to form the general relativity (GR) theory. ...
For a less technical introduction to this topic, please see Introduction to mathematics of general relativity. ...
The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and welldefined state of rest...
In the physics of relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...
In physics, the world line of an object is the unique path of that object as it travels through 4dimensional spacetime. ...
In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ...
In general relativity, the Kepler problem involves solving for the motion of a particle of negligible mass in the external gravitational field of another body of mass M. This gravitational field is described by the Schwarzschild solution to the vacuum Einstein equations of general relativity, and particle motion is described...
This article or section is in need of attention from an expert on the subject. ...
For the concept in fluid dynamics and meteorology, see Gravity wave. ...
According to Albert Einsteins theory of general relativity, space and time get pulled out of shape near a rotating body in a phenomenon referred to as framedragging. ...
The geodetic effect represents the effect of the curvature of spacetime, predicted by general relativity, on a spinning, moving body. ...
A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. ...
Simulated view of a black hole in front of the Milky Way. ...
 Equations  Linearized Gravity PostNewtonian formalism Einstein field equations  Advanced theories  KaluzaKlein Quantum gravity  Solutions  Schwarzschild ReissnerNordström Kerr · KerrNewman Kasner · Milne · RobertsonWalker It has been suggested that Weakfield approximation be merged into this article or section. ...
The parameterized postNewtonian formalism or PPN formalism is a tool used to compare classical theories of gravitation in the limit most important for everyday gravitational experiments: the limit in which the gravitational field is weak and generated by objects moving slowly compared to the speed of light. ...
This article or section is in need of attention from an expert on the subject. ...
KaluzaKlein theory (or KK theory, for short) is a model which sought to unify classical gravity and electromagnetism. ...
This article does not cite any references or sources. ...
It has been suggested that Deriving the Schwarzschild solution be merged into this article or section. ...
In physics and astronomy, a ReissnerNordstrÃ¶m black hole, discovered by Gunnar NordstrÃ¶m and Hans Reissner, is a black hole that carries electric charge , no angular momentum, and mass . ...
In general relativity, the Kerr metric (or Kerr vacuum) describes the geometry of spacetime around a rotating massive body, such as a rotating black hole. ...
The KerrNewman metric is a solution of Einsteins general relativity field equation that describes the spacetime geometry around a charged (), rotating () black hole of mass m. ...
The Kasner metric is an exact solution to Einsteins theory of general relativity. ...
Milnes model follows the description from special relativity of an observable universes spacetime diagram containing past and future light cones along with elsewhere in spacetime. ...
// The FriedmannLemaÃ®treRobertsonWalker (FLRW) metric is an exact solution of the Einstein field equations of general relativity and which describes a homogeneous, isotropic expanding/contracting universe. ...
 Scientists  Einstein · Minkowski · Eddington Lemaître · Schwarzschild Robertson · Kerr · Friedman Chandrasekhar · Hawking · others â€œEinsteinâ€ redirects here. ...
Hermann Minkowski. ...
One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the Englishspeaking world. ...
Father GeorgesHenri LemaÃ®tre (July 17, 1894 â€“ June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer. ...
Karl Schwarzschild (October 9, 1873  May 11, 1916) was a noted German Jewish physicist and astronomer, father of astrophysicist Martin Schwarzschild. ...
Howard Percy Robertson (January 27, 1903  August 26, 1961) was a scientist known for contributions related to cosmology and the uncertainty principle. ...
Roy Patrick Kerr (1934 ) is a New Zealand born mathematician who is best known for discovering the famous Kerr vacuum, an exact solution to the Einstein field equation of general relativity, which models the gravitational field outside an uncharged rotating massive object, or even a rotating black hole. ...
Alexander Alexandrovich Friedman or Friedmann (ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€ ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ€Ð¾Ð²Ð¸Ñ‡ Ð¤Ñ€Ð¸Ð´Ð¼Ð°Ð½) (June 16, 1888 â€“ September 16, 1925) was a Russian cosmologist and mathematician. ...
Chandrasekhar redirects here. ...
Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...
This is a partial list of persons who have made major contributions to the development of standard mainstream general relativity. ...
 This box: view • talk • edit  In general relativity, event horizon is a general term for a boundary in spacetime, defined with respect to an observer, beyond which events cannot affect the observer. Light emitted from beyond the horizon can never reach the observer, and anything that passes through the horizon from the observer's side is never seen again. A black hole is surrounded by an event horizon, for example. This article needs additional references or sources for verification. ...
Event Horizon is a 1997 science fiction horror film that was directed by Paul W. S. Anderson and written by Philip Eisner (with an uncredited rewrite by Andrew Kevin Walker). ...
An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ...
In physics, spacetime is any mathematical model that combines space and time into a single construct called the spacetime continuum. ...
This article does not cite any references or sources. ...
Simulated view of a black hole in front of the Milky Way. ...
More specific types of horizons include the related but distinct absolute and apparent horizons found around a black hole. Still other distinct notions include the Cauchy and Killing horizon; the photon spheres and ergospheres of the ReissnerNordström solution; particle and cosmological horizons relevant to cosmology; and isolated and dynamical horizons important in current black hole research. In general relativity, an absolute horizon is a boundary in spacetime, defined with respect to the external universe, inside of which events cannot affect an external observer. ...
An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards. ...
In physics, a Cauchy horizon is a light_like boundary of the domain of validity of a Cauchy problem. ...
Astronomy A common case of a Killing horizon in astrophysics occurs as part of a rotating black hole and is a surface on which the rotational killing vector field becomes null. ...
A photon sphere is a spherical region of space surrounding extremely massive objects such as black holes. ...
A rotating black hole (Kerr black hole or KerrNewman black hole) is a black hole that possesses angular momentum. ...
In physics and astronomy, a ReissnerNordstrÃ¶m black hole, discovered by Gunnar NordstrÃ¶m and Hans Reissner, is a black hole that carries mass , electric charge , and no angular momentum. ...
It has been suggested that this article or section be merged into Observable universe. ...
In cosmology, a cosmological horizon marks a limit to observability, and marks the boundary of a region that an observer cannot see into directly due to cosmological effects. ...
Cosmology, from the Greek: ÎºÎ¿ÏƒÎ¼Î¿Î»Î¿Î³Î¯Î± (cosmologia, ÎºÏŒÏƒÎ¼Î¿Ï‚ (cosmos) order + Î»Î¿Î³Î¹Î± (logia) discourse) is the study of the Universe in its totality, and by extension, humanitys place in it. ...
Event horizon of a black hole 
The most commonly known example of an event horizon is defined around general relativity's description of a black hole, a celestial object dense enough that its gravitational field is so strong that no matter or radiation can escape. This is sometimes described as the boundary within which the black hole's escape velocity is greater than the speed of light. While this definition can be made to work, it only does so if the effects of special and general relativity are taken into account. A more accurate description is to note that within this horizon, all lightlike paths (paths light could take), and hence all paths in the forward light cones of particles within the horizon, are warped so as to fall further into the hole. Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time (and can actually be thought of as equivalent to doing so, depending on the spacetime coordinate system used). Simulated view of a black hole in front of the Milky Way. ...
Simulated view of a black hole in front of the Milky Way. ...
Space Shuttle Atlantis launches on mission STS71. ...
A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic...
In physics, the adjective lightlike refers to a contour in spacetime in the context of special relativity whose proper length vanishes. ...
In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ...
The surface at the Schwarzschild radius acts as an event horizon in a nonrotating body that fits inside this radius. (A rotating black hole operates slightly differently.) The Schwarzschild radius of an object is proportional to the mass. For the mass of the Sun it is approximately 3 km, and for that of the Earth about 9 mm. For a black hole created by the collapse of a star (which has a mass above the Chandrasekhar limit) the lower limit is about 4 km. The Schwarzschild radius (sometimes inappropriately referred to as the gravitational radius[1]) is a characteristic radius associated with every mass. ...
A rotating black hole (Kerr black hole or KerrNewman black hole) is a black hole that possesses angular momentum. ...
The Sun (Latin: Sol) is the star at the center of the Solar System. ...
This article is about Earth as a planet. ...
The Chandrasekhar limit, is the maximum mass possible for a white dwarf (one of the end stages of stars when they cool down) and is approximately 3 Ã— 1030 kg, around 1. ...
Black hole event horizons are especially noteworthy for three reasons. First, there are many examples near enough to study. Second, black holes tend to pull in matter from their environment, which provides examples where matter passing through an event horizon is expected to be observable. Third, the description of black holes given by general relativity is known to be an approximation, with quantum gravity effects expected to become significant near the vicinity of the event horizon. This allows observations of matter in the vicinity of a black hole's event horizon to be used to indirectly study general relativity and proposed extensions to it. This article does not cite any references or sources. ...
An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ...
The definition of "event horizon" given by Hawking & Ellis^{[1]}, Misner, Thorne & Wheeler^{[2]}, and Wald^{[3]} differs from the one presented here. Their definition of an event horizon rules out the cosmological and particle horizons presented below (as well as the apparent horizon). However, modern usage has brought those ideas under the umbrella of the term "event horizon". (See, e.g., ^{[4]}.) To make the distinction clearer, some authors refer to their more specific notion of a horizon as an "absolute horizon". In the context of black holes, event horizon almost always refers to the absolute horizon, as distinct from the apparent horizon. An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards. ...
In general relativity, an absolute horizon is a boundary in spacetime, defined with respect to the external universe, inside of which events cannot affect an external observer. ...
Event horizon of the observable universe 
The particle horizon of the observable universe is the boundary that represents the maximum distance at which events can currently be observed. For events beyond that distance, light hasn't had time to reach our location, even if it were emitted at the time the universe began. How the particle horizon changes with time depends on the nature of the expansion of the universe. If the expansion has appropriate characteristics, there are parts of the universe that will never be observable, no matter how long the observer waits for light from those regions to arrive. The boundary past which events can't ever be observed is an event horizon, and represents the maximum extent of the particle horizon. This article does not cite any references or sources. ...
It has been suggested that this article or section be merged into Observable universe. ...
See universe for a general discussion of the universe. ...
Wikipedia does not yet have an article with this exact name. ...
The criterion for determining whether an event horizon for the universe exists is as follows. Define a comoving distance d_{E} by The comoving distance or conformal distance of two objects in the universe is the distance divided by a timevarying scale factor representing the expansion of the universe. ...

In this equation, a is the scale factor, c is the speed of light, and t_{0} is the age of the universe. If , points arbitrarily far away can be observed, and no event horizon exists. If , a horizon is present. The scale factor, parameter of FriedmannLemaÃ®treRobertsonWalker model, is a function of time which represents the relative expansion of the universe. ...
A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic...
Examples of cosmological models without an event horizon are universes dominated by matter or by radiation. An example of a cosmological model with an event horizon is a universe dominated by the cosmological constant (a de Sitter universe). Matter is the substance of which physical objects are composed. ...
This article does not cite any references or sources. ...
In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Î›) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ...
A de Sitter universe is a solution to Einsteins field equations of General Relativity which is named after Willem de Sitter. ...
Event horizon of an accelerated particle
Spacetime diagram showing a uniformly accelerated particle, P, and an event E that is outside the particle's event horizon. The event's forward light cone never intersects the particle's world line. If a particle is moving at a constant velocity in a nonexpanding universe free of gravitational fields, any event that occurs in that universe will eventually be observable by the particle, because the forward light cones from these events intersect the particle's world line. On the other hand, if the particle is accelerating, it's possible to construct situations where light cones from some events never intersect the particle's world line. Under these conditions, an event horizon is present in the particle's (accelerating) reference frame, representing a boundary beyond which events are unobservable. Image File history File links This is a lossless scalable vector image. ...
Image File history File links This is a lossless scalable vector image. ...
In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ...
In physics, the world line of an object is the unique path of that object as it travels through 4dimensional spacetime. ...
In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ...
In physics, the world line of an object is the unique path of that object as it travels through 4dimensional spacetime. ...
One situation where this occurs is the case of a uniformly accelerated particle. A spacetime diagram of this situation is shown in the figure to the right. As the particle accelerates, it approaches, but never reaches, the speed of light with respect to its original reference frame. On the spacetime diagram, its path is a hyperbola, which asymptotically approaches a 45 degree line (the path of a light ray). An event whose light cone's edge is this asymptote or is farther away than this asymptote can never be observed by the accelerating particle. In the particle's reference frame, there appears to be a boundary behind it from which no signals can escape (an event horizon). In mathematics, a hyperbola (Greek literally overshooting or excess) is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone. ...
An asymptote is a straight line or curve which a curve approaches as one moves along the curve. ...
While approximations of this type of situation can occur in the real world (in particle accelerators, for example), a true event horizon is never present, as the particle must be accelerated indefinitely (requiring arbitrarily large amounts of energy and an arbitrarily large apparatus). For the DC Comics Superhero also called Atom Smasher, see Albert Rothstein. ...
Interacting with an event horizon A misconception concerning event horizons, especially black hole event horizons, is that they represent an immutable surface that destroys objects that approach them. In practice, several features are common to all event horizons: they appear to be some distance away from any observer, and objects sent towards an event horizon never appear to cross it from the sending observer's point of view (as the horizoncrossing event's light cone never intersects the observer's world line). Attempting to make an object approaching the horizon remain stationary with respect to an observer requires applying a force whose magnitude becomes unbounded (becoming infinite) the closer it gets. Simulated view of a black hole in front of the Milky Way. ...
In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ...
In physics, the world line of an object is the unique path of that object as it travels through 4dimensional spacetime. ...
For the case of a horizon perceived by a uniformly accelerating observer in empty space, the horizon seems to remain a fixed distance from the observer no matter how its surroundings move. Varying the observer's acceleration may cause the horizon to appear to move over time, or may prevent an event horizon from existing, depending on the acceleration function chosen. The observer never touches the horizon, and never passes a location where it appeared to be. For the case of a horizon perceived by an occupant of a de Sitter universe, the horizon always appears to be a fixed distance away for a nonaccelerating observer. It is never contacted, even by an accelerating observer. A de Sitter universe is a solution to Einsteins field equations of General Relativity which is named after Willem de Sitter. ...
An inertial reference frame is one in which Newtons first and second laws of motion are valid. ...
For the case of the horizon around a black hole, observers stationary with respect to a distant object will all agree on where the horizon is. While this seems to allow an observer lowered towards the hole on a rope to contact the horizon, in practice this cannot be done. If the observer is lowered very slowly, then, in the observer's frame of reference, the horizon appears to be very far away, and ever more rope needs to be paid out to reach the horizon. If the observer is lowered quickly, then indeed the observer, and some of the rope can touch and even cross the (distant lowerer's) event horizon. If the rope is pulled taut to fish the observer back out, then the forces along the rope increase without bound as they approach the event horizon, and at some point the rope must break. Furthermore, the break must occur not at the event horizon, but at a point where the lowerer can observe it. Attempting to stick a rigid rod through the hole's horizon cannot be done: if the rod is lowered extremely slowly, then it is always too short to touch the event horizon, as the coordinate frames near the tip of the rod are extremely compressed. From the point of view of an observer at the end of the rod, the event horizon remains hopelessly out of reach. If the rod is lowered quickly, then the same problems as with the rope are encountered: the rod must break and the broken off pieces inevitably fall in. These peculiarities only occur because of the supposition that the observers be stationary with respect to some other distant observer. Observers that fall into the hole are moving with respect to the distant observer, and so perceive the horizon as being in a different location, seeming to recede in front of them so that they never contact it. Increasing tidal forces (and eventual impact with the hole's gravitational singularity) are the only locally noticeable effects. While this seems to allow an infalling observer to relay information from objects outside their perceived horizon but inside the distant observer's perceived horizon, in practice the horizon recedes by an amount small enough that by the time the infalling observer receives any signal from farther into the hole, they've already crossed what the distant observer perceived to be the horizon, and this reception event (and any retransmission) can't be seen by the distant observer. Comet ShoemakerLevy 9 after breaking up under the influence of Jupiters tidal forces. ...
A gravitational singularity (sometimes spacetime singularity) is, approximately, a place where quantities which are used to measure the gravitational field become infinite. ...
Event horizons beyond general relativity The description of event horizons given by general relativity is thought to be incomplete. When the conditions under which event horizons occur are modelled using a more complete picture of the way the universe works, that includes both relativity and quantum mechanics, event horizons are expected to have properties that are different from those predicted using general relativity alone. An illustration of a rotating black hole at the center of a galaxy General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ...
Fig. ...
At present, the primary expected impact of quantum effects is for event horizons to possess a temperature, and emit radiation as a result. For black holes, this manifests as Hawking radiation, and the larger question of how the black hole possesses a temperature is part of the topic of black hole thermodynamics. For accelerating particles, this manifests as the Unruh effect, which causes space around the particle to appear to be filled with matter and radiation. This article includes a list of works cited or a list of external links, but its sources remain unclear because it lacks intext citations. ...
Simulated view of a black hole in front of the Milky Way. ...
In physics, Hawking radiation (also known as BekensteinHawking radiation) is a thermal radiation thought to be emitted by black holes due to quantum effects. ...
This article or section is in need of attention from an expert on the subject. ...
The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe blackbody radiation where an inertial observer would observe none, that is, the accelerating observer will find themselves in a warm background. ...
A complete description of event horizons is expected to at minimum require a theory of quantum gravity. As of 2006, the most promising candidate theory is Mtheory. This article does not cite any references or sources. ...
2006 is a common year starting on Sunday of the Gregorian calendar. ...
Mtheory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11dimensional supergravity together. ...
See also In mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region â€“ essentially describing the intrinsic geometry of the region. ...
This article is in need of attention. ...
References The Universe in a Nutshell is one of Stephen Hawkings latest books on theoretical physics. ...
Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...
More technical references  ^ S. W. Hawking and G. F. R. Ellis (1975). The large scale structure of spacetime. Cambridge University Press.
 ^ Thorne, Kip S.; Misner, Charles; Wheeler, John (1973). Gravitation. W. H. Freeman and Company.
 ^ Wald, Robert M. (1984). General Relativity. Chicago: University of Chicago Press.
 ^ J. A. Peacock (1999). Cosmological Physics. Cambridge University Press.
