General relativity
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For the graduate textbook by Robert Wald, see General Relativity (book).
For a more accessible and less technical introduction to this topic, see Introduction to
general relativity.
Part of a series of articles about
General relativity
o Introduction
o History
Mathematical formulation
o Tests
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Fundamental concepts
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Phenomena
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Equations
Formalisms
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Solutions
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Theorems
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Scientists
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Slow motion computer simulation of the black hole binary system GW150914 as seen by a nearby observer,
during 0.33 s of its final inspiral, merge, and ringdown. The star field behind the black holes is being heavily
distorted and appears to rotate and move, due to extreme gravitational lensing, as spacetime itself is distorted
and dragged around by the rotating black holes.[1]
General relativity, also known as the general theory of relativity, 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 partial differential equations.
Some predictions of general relativity differ significantly from those of classical physics,
especially concerning the passage of time, the geometry of space, the motion of bodies
in free fall, and the propagation of light. Examples of such differences
include gravitational time dilation, gravitational lensing, the gravitational redshift of light,
the gravitational time delay and singularities/black holes. The predictions of general
relativity in relation to classical physics have been confirmed in all observations and
experiments to date. Although general relativity is not the only relativistic theory of
gravity, it is the simplest theory that is consistent with experimental data. However,
unanswered questions remain, the most fundamental being how general relativity can
be reconciled with the laws of quantum physics to produce a complete and self-
consistent theory of quantum gravity, how gravity can be unified with the three non-
gravitational forces—strong nuclear, weak nuclear, and electromagnetic forces.
Einstein's theory has important astrophysical implications. For example, it implies the
existence of black holes—regions of space in which space and time are distorted in
such a way that nothing, not even light, can escape—as an end-state for massive stars.
There is ample evidence that the intense radiation emitted by certain kinds of
astronomical objects is due to black holes. For example, microquasars and active
galactic nuclei result from the presence of stellar black holes and supermassive black
holes, respectively. The bending of light by gravity can lead to the phenomenon of
gravitational lensing, in which multiple images of the same distant astronomical object
are visible in the sky. General relativity also predicts the existence of gravitational
waves, which have since been observed directly by the physics collaboration LIGO. In
addition, general relativity is the basis of current cosmological models of a
consistently expanding universe.
Widely acknowledged as a theory of extraordinary beauty, general relativity has often
been described as the most beautiful of all existing physical theories. [2]
Contents
1History
2From classical mechanics to general relativity
o 2.1Geometry of Newtonian gravity
o 2.2Relativistic generalization
o 2.3Einstein's equations
o 2.4Total force in general relativity
o 2.5Alternatives to general relativity
3Definition and basic applications
o 3.1Definition and basic properties
o 3.2Model-building
4Consequences of Einstein's theory
o 4.1Gravitational time dilation and frequency shift
o 4.2Light deflection and gravitational time delay
o 4.3Gravitational waves
o 4.4Orbital effects and the relativity of direction
5Astrophysical applications
o 5.1Gravitational lensing
o 5.2Gravitational-wave astronomy
o 5.3Black holes and other compact objects
o 5.4Cosmology
o 5.5Time travel
6Advanced concepts
o 6.1Asymptotic symmetries
o 6.2Causal structure and global geometry
o 6.3Horizons
o 6.4Singularities
o 6.5Evolution equations
o 6.6Global and quasi-local quantities
7Relationship with quantum theory
o 7.1Quantum field theory in curved spacetime
o 7.2Quantum gravity
8Current status
9See also
10References
11Bibliography
12Further reading
o 12.1Popular books
o 12.2Beginning undergraduate textbooks
o 12.3Advanced undergraduate textbooks
o 12.4Graduate textbooks
o 12.5Specialists' books
o 12.6Journal articles
13External links
History[edit]
Main articles: History of general relativity and Classical theories of gravitation
Soon after publishing the special theory of relativity in 1905, Einstein started thinking
about how to incorporate gravity into his new relativistic framework. In 1907, beginning
with a simple thought experiment involving an observer in free fall, he embarked on
what would be an eight-year search for a relativistic theory of gravity. After numerous
detours and false starts, his work culminated in the presentation to the Prussian
Academy of Science in November 1915 of what are now known as the Einstein field
equations, which form the core of Einstein's general theory of relativity. [3] These
equations specify how the geometry of space and time is influenced by
