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General relativity

General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is 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 four-dimensional spacetime. In particular, the 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 second order partial differential equations.

For the graduate textbook by Robert Wald, see General Relativity (book).

Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitation in classical physics. These predictions concern the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light, and include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the Shapiro time delay and singularities/black holes. So far, all tests of general relativity have been shown to be in agreement with the theory. The time-dependent solutions of general relativity enable us to talk about the history of the universe and have provided the modern framework for cosmology, thus leading to the discovery of the Big Bang and cosmic microwave background radiation. Despite the introduction of a number of alternative theories, general relativity continues to be the simplest theory consistent with experimental data.


Reconciliation of general relativity with the laws of quantum physics remains a problem, however, as there is a lack of a self-consistent theory of quantum gravity. It is not yet known how gravity can be unified with the three non-gravitational forces: strong, weak and electromagnetic.


Einstein's theory has astrophysical implications, including the prediction of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape from them. Black holes are the end-state for massive stars. Microquasars and active galactic nuclei are believed to be stellar black holes and supermassive black holes. It also predicts gravitational lensing, where the bending of light results in multiple images of the same distant astronomical phenomenon. Other predictions include the existence of gravitational waves, which have been observed directly by the physics collaboration LIGO and other observatories. In addition, general relativity has provided the base of cosmological models of an 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.[2]

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orbital eccentricity

 – Hypothetical FTL transportation by warping space (warp drive)

Alcubierre drive

 – Proposed theories of gravity

Alternatives to general relativity

Contributors to general relativity

Derivations of the Lorentz transformations

 – Paradox in special relativity

Ehrenfest paradox

 – Concept in general relativity

Einstein–Hilbert action

 – Albert Einstein's hypothetical situations to argue scientific points

Einstein's thought experiments

 – Debate about credit for general relativity

General relativity priority dispute

 – non-technical introduction to the mathematics of general relativity

Introduction to the mathematics of general relativity

 – Predecessor to the theory of relativity

Nordström's theory of gravitation

 – Tensor index notation for tensor-based calculations

Ricci calculus

Timeline of gravitational physics and relativity

(1916), Relativity: The Special and the General Theory, Berlin, ISBN 978-3-528-06059-6{{citation}}: CS1 maint: location missing publisher (link)

Einstein, A.

(1981), General Relativity from A to B, Chicago: University of Chicago Press, ISBN 978-0-226-28864-2

Geroch, R.

(2008), The Einstein Theory of Relativity: A Trip to the Fourth Dimension, Philadelphia: Paul Dry Books, Inc., ISBN 978-1-58988-044-3

Lieber, Lillian

(2001), "Gravitational radiation", in Murdin, Paul (ed.), Encyclopedia of Astronomy and Astrophysics, Institute of Physics Pub., ISBN 978-1-56159-268-5

Schutz, Bernard F.

; Hawking, Stephen (1994). Black Holes and Time Warps: Einstein's Outrageous Legacy. New York: W. W. Norton. ISBN 0-393-03505-0.

Thorne, Kip

(1992), Space, Time, and Gravity: the Theory of the Big Bang and Black Holes, Chicago: University of Chicago Press, ISBN 978-0-226-87029-8

Wald, Robert M.

; Ford, Kenneth (1998), Geons, Black Holes, & Quantum Foam: a life in physics, New York: W. W. Norton, ISBN 978-0-393-31991-0

Wheeler, John

Archived 1 June 2014 at the Wayback Machine – Articles on a variety of aspects of relativistic physics for a general audience; hosted by the Max Planck Institute for Gravitational Physics

Einstein Online

the official website of the GEO600 project.

GEO600 home page

LIGO Laboratory

 – produced by the numerical relativity group at the NCSA, with an elementary introduction to general relativity

NCSA Spacetime Wrinkles