General relativity

Overview of GR History Mathematics Resources Tests Black hole Einstein equation Equivalence principle Event horizon Exact solutions FLRW metric Gravitational lens Gravitational radiation Kerr metric Quantum gravity Schwarzschild metric Singularity

Related topics

Albert Einstein Astrophysics Gravity Cosmology Special relativity Riemannian geometry

edit It has been suggested that Einsteins theory of gravitation be merged into this article or section. ... Image File history File links Download high resolution version (1024x768, 7 KB) Description: Gravitational light deflection at a neutron star Source: Gallery of Tempolimit Lichtgeschwindigkeit Date: 09. ... It has been suggested that Einsteins theory of gravitation be merged into this article or section. ... Notational point: General relativity articles using tensors will use the abstract index notation . ... // Books Popular Geroch, Robert (1981). ... Einsteins general theory of relativity was introduced in 1915. ... A black hole is a concentration of mass great enough that the force of gravity prevents anything past its event horizon from escaping it except through quantum tunnelling behaviour (known as Hawking Radiation). ... In physics, the Einstein field equation or Einstein equation is a differential equation in Einsteins theory of general relativity. ... THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... Event Horizon is a 1997 science fiction and horror film. ... // In general relativity, an exact solution is a Lorentzian manifold equipped with certain tensor fields which are taken to model states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field. ... The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ... This article is in need of attention from an expert on the subject. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In general relativity, the Kerr metric describes the geometry of spacetime around a rotating massive body, such as a rotating black hole. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... It has been suggested that Deriving the Schwarzschild solution be merged into this article or section. ... This article is in need of attention from an expert on the subject. ... Albert Einstein, photographed by Oren J. Turner in 1947. ... Spiral Galaxy ESO 269-57 // Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature and chemical composition) of astronomical objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... Gravity is a force of attraction that acts between bodies that have mass. ... Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. It replaced Newtonian notions of space and time and incorporated electromagnetism as represented by Maxwells equations. ... In mathematics, Riemannian geometry has at least two meanings, one of which is described in this article and another also called elliptic geometry. ...

Creation of General Relativity

Early investigations

The development of general relativity began in 1907 with the publication of an article by Albert Einstein on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the Equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation. In 1911, Einstein published another article expanding on the 1907 article, in which additional effects such as the deflection of light by massive bodies were predicted. It has been suggested that Einsteins theory of gravitation be merged into this article or section. ... 1907 (MCMVII) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 13-day-slower Julian calendar). ... Albert Einstein, photographed by Oren J. Turner in 1947. ... Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. It replaced Newtonian notions of space and time and incorporated electromagnetism as represented by Maxwells equations. ... Free-fall or free fall in the strict sense is the condition of acceleration which is due only to gravity. ... THERE IS NO SUCH THING< MWAHAHAHAHAHAHAHA> In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... Gravitational time dilation is a consequence of Albert Einsteins theories of relativity and related theories under which a clock at a different gravitational potential is found to tick at a different rate than ones own clock. ... 1911 (MCMXI) was a common year starting on Sunday (click on link for calendar). ... A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is bent around a massive object (such as a massive galaxy) between the source object and the observer. ...

General covariance and the hole argument

By 1912, Einstein was actively seeking a theory in which gravitation was explained as a geometric phenomenon. At the urging of Levi-Civita, Einstein began by exploring the use of general covariance (which is essentially the use of curvature tensors) to create a gravitational theory. However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "hole argument". In 1914 and much of 1915, Einstein was trying to create field equations based on another approach. When that approach was proven to be inconsistent, Einstein revisited the concept of general covariance and discovered that the hole argument was flawed. In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. ... Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Theaetetus dealing with spatial relationships. ... Tullio Levi-Cività (March 29, 1873 - December 29, 1941) was an Italian mathematician, most famous for his work on tensor calculus but who also made significant contributions in other areas, some related to this work and some not. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... For more technical Wiki articles on tensors, see the section later in this article. ... 1913 (MCMXIII) was a common year starting on Wednesday. ... This article is in need of attention from an expert on the subject. ... A field equation is an equation in a physical theory that describes how a fundamental force (or a combination of such forces) interacts with matter. ...

The development of the Einstein Field Equations

When Einstein realized that general covariance was actually tenable, he quickly completed the development of the field equations that are named after him. However, he made a now-famous mistake. The field equations he published in October of 1915 were

,

where R_μν is the Ricci tensor, and T_μν the energy-momentum tensor. This predicted the non-Newtonian perihelion precession of Mercury, and so had Einstein very excited. However, it was soon realized that they were inconsistent with the local conservation of energy-momentum unless the universe had a constant density of mass-energy-momentum. In other words, air, rock and even a vacuum should all have the same density! This inconsistency with observation sent Einstein back to the drawing board. However, the solution was all but obvious, and in November of 1915 Einstein published the actual Einstein field equations: In differential geometry, the Ricci curvature tensor is (0,2)-valent tensor, obtained as a trace of the full curvature tensor. ... The stress tensor or energy-momentum tensor is the corresponding conserved Noether current of any theory which is invariant under spacetime translations. ... The newton (symbol: N) is the SI unit of force. ... Precession refers to a change in the direction of the axis of a rotating object. ... Atmospheric characteristics Atmospheric pressure trace Potassium 31. ...

,

where R is the Ricci scalar and g_μν the metric tensor. With the publication of the field equations, the issue became one of solving them for various cases and interpreting the solutions. This and experimental verification have dominated general relativity research ever since. In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest way of describing the curvature of a Riemannian manifold. ... In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space. ...

Einstein and Hilbert

Although Einstein is credited with finding the field equations, the German mathematician David Hilbert published them in an article before Einstein's article. This has resulted in accusations of plagiarism against Einstein, and assertions that the field equations should be called the "Einstein-Hilbert field equations". However, Hilbert did not press his claim for priority, and recent research has shown that Einstein submitted the correct equations before Hilbert amended his own work to include them. This suggets that Einstein developed the correct field equations first, though Hilbert may have reached them later independently (or even learned of them afterwards through his correspondence with Einstein). ^[1] Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that did not include references to the work of others. ... David Hilbert David Hilbert (January 23, 1862, Wehlau, East Prussia–February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... Plagiarism is a form of academic dishonesty, the unacknowledged use of another persons idea(s), information, language or writing. ...

Solutions

The Schwarzschild solution

Since the field equations are non-linear, Einstein assumed that they were insoluble. However, 1916 Karl Schwarzschild discovered an exact solution for the case of a spherically symmetric spacetime surrounding a massive object in spherical coordinates. This is now known as the Schwarzschild solution. Since then, many other exact solutions have been found. To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... 1916 (MCMXVI) was a leap year starting on Saturday (link will take you to calendar). ... Karl Schwarzschild (October 9, 1873 - May 11, 1916) was a noted German Jewish physicist and astronomer, father of astrophysicist Martin Schwarzschild. ... Category: Mathematics stubs ... World line of the orbit of the Earth depicted in two spatial dimensions X and Y (the plane of the Earth orbit) and a time dimension, usually put as the vertical axis. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... Introduction In Einsteins theory of general relativity, the Schwarzschild metric is the most general static, spherically symmetric solution of the vacuum field equations. ...

The expanding universe and the cosmological constant

In 1922, Alexander Friedmann found a solution in which the universe may expand or contract, and later Georges Lemaître derived a solution for an expanding universe. However, Einstein did not believe in an expanding universe, and so he added in a cosmological constant Λ to his field equations. The revised field equations were 1922 (MCMXXII) was a common year starting on Sunday (see link for calendar). ... Alexander Alexandrovich Friedman (June 16, 1888 – September 16, Russian cosmologist and mathematician. ... Father Georges-Henri Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest and astronomer. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ...

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This permitted the creation of steady-state solutions, but they were never stable solutions: the slightest deviation from an ideal state would still result in the universe expanding or contracting. In 1929, Edwin Hubble found evidence for the idea that the universe is expanding. This resulted in Einstein dropping the cosmological constant, referring to it as "the biggest blunder in my career". One may notice that, at the time, it was an ad hoc hypothesis to add in the cosmological constant, as it was only intended to explain one result (an apparently static universe). 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ... Edwin Hubble Edwin Powell Hubble (November 20, 1889–September 28, 1953) was an American astronomer, noted for his discovery of galaxies beyond the Milky Way and the cosmological redshift. ... Ad hoc is a Latin phrase which means for this [purpose]. It generally signifies a solution that has been tailored to a specific purpose, such as a tailor-made suit, a handcrafted network protocol, and specific-purpose equation and things like that. ...

More exact solutions

Progress in solving the field equations and understanding the solutions has been ongoing. The solution for a spherically symmetric charged object was discovered by Reissner and later rediscovered by Nordström, and is called the Reissner-Nordström solution. The black hole aspect of the Schwarzschild solution was very controversial, and Einstein did not believe it. However, in 1957 (two years after Einstein's death in 1955), Kruskal published a proof that black holes are called for by the Schwarzschild Solution. Additionally, the solution for a rotating massive object was obtained by Kerr in the 1960's and is called the Kerr solution. The Kerr-Newman solution for a rotating, charged massive object was published a few years later. In physics and astronomy, a Reissner-Nordström black hole, discovered by Gunnar Nordström and Hans Reissner, is a black hole that carries electric charge , no angular momentum, and mass . ... 1957 (MCMLVII) was a common year starting on Tuesday of the Gregorian calendar. ... 1955 (MCMLV) was a common year starting on Saturday of the Gregorian calendar. ... People named Kerr: Alex Kerr, Japanologist Alfred Kerr, german journalist, critic and writer Archibald John Kerr Clark Kerr, 1st Baron Inverchapel, British diplomat Baine Kerr, Huston lawyer Ben Kerr, Canadian author Bill Kerr, actor Bobby Kerr, Irish-Canadian sprinter Brian Kerr, Irish soccer manager Brooke Kerr; American actress Clark Kerr... In general relativity, the Kerr metric describes the geometry of spacetime around a rotating massive body, such as a rotating black hole. ... The Kerr-Newman metric is a solution of Einsteins general relativity field equation that describes the spacetime geometry around a charged (), rotating () black hole of mass m. ...

Testing the theory

The perihelion precession of Mercury was the first evidence that general relativity is correct. Eddington's 1919 expedition in which he confirmed Einstein's prediction for the deflection of light by the Sun helped to cement the status of general relativity as a likely true theory. Since then many observations have confirmed the correctness of general relativity. These include studies of binary pulsars, observations of radio signals passing the limb of the Sun, and even the GPS system. For more information, see the Tests of general relativity article. Eddington is the name of several places United States of America Eddington, Maine Eddington, Pennsylvania United Kingdom Eddington, Berkshire Eddington, Kent Edington, Somerset Edington, Wiltshire Also see: Arthur Eddington, an important astrophysicist This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same... It has been suggested that Einsteins theory of gravitation be merged into this article or section. ... Wikipedia does not yet have an article with this exact name. ... Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ... Einsteins general theory of relativity was introduced in 1915. ...

Alternative theories

Finally, there have been various attempts through the years to find modifications to general relativity. The most famous of these are the Brans-Dicke theory (also known as scalar-tensor theory), and Rosen's bimetric theory. Both of these proposed changes to the field equations, and both suffer from these changes permitting the presence of bipolar gravitational radiation. As a result, Rosen's original theory has been refuted by observations of binary pulsars. As for Brans-Dicke (which has a tunable parameter ω such that ω = ∞ is the same as general relativity), the amount by which it can differ from general relativity has been severely constrained by these observations. However, general relativity and quantum mechanics (a theory that has been experimentally verified more than GR) are known to be inconsistent. Much speculation exists that modifications of GR (but not QM) are needed on the smallest scales (as GR has not been tested rigorously on the smallest scales). In the other camp, speculation exists that QM needs to be modified [for example, it usually assumes a fixed (flat) spacetime background]. Most researchers believe that both theories are in need of modification. In mathematical physics, the Brans-Dicke theory of gravitation (sometimes called the Jordan/Brans/Dicke theory) is a well-known competitor of Einsteins theory of general relativity. ... This article is in need of attention from an expert on the subject. ... A simple introduction to this subject is provided in Basics of quantum mechanics. ...

See also

• Priority disputes about Einstein and the relativity theories

Albert Einstein presented the theories of Special Relativity and General Relativity in groundbreaking publications that did not include references to the work of others. ...

Notes

1. ^ Reference: "Belated Decision in the Hilbert-Einstein Priority Dispute" by Leo Corry, Jürgen Renn, and John Stachel; Science 14 November 1997: Vol. 278. no. 5341, pp. 1270 - 1273 [1], [2]

References

• Pais, Abraham (1982). Subtle is the lord: the science and life of Albert Einstein. Oxford: Oxford University Press. ISBN 0-198-53907-X.
• Genesis of general relativity series
• * Leo Corry, Jürgen Renn, John Stachel: "Belated Decision in the Hilbert-Einstein Priority Dispute", SCIENCE, Vol. 278, 14 November 1997 - article text
• Friedwart Winterberg's response to the Cory-Renn-Stachel paper as printed in "Zeitschrift für Naturforschung" 59a, 715-719.