General relativity

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Elevator gravity

Light cone

Gravitational red-shifting

Light deflection

General Relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions from many others after 1915. The theory generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or 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.

Overview

In general relativity, the distribution of matter and energy determines the geometry of spacetime, which in turn describes the acceleration of matter. Therefore, solutions of the Einstein field equations describe the evolution of the universe, the properties of black holes, the bending of light by gravity, and the physics of neutron stars, among other phenomena.

History

The history of general relativity began with the publication of Einstein's paper "The Foundation of the General Theory of Relativity" in 1916, which provided a radically new way to understand gravity, different from the Newtonian physics that had been used since the 17th century. Einstein's theory was confirmed by observations such as the 1919 solar eclipse that showed the bending of light around the sun, thus providing strong evidence for general relativity over Newtonian gravity.

Mathematical Formulation

The mathematical formulation of general relativity is based on the Einstein field equations (EFE), which relate the geometry of spacetime with the distribution of matter within it. Solutions to the EFE provide descriptions of the gravitational field and the metric tensor, which defines the spacetime geometry. The theory uses the mathematics of differential geometry and tensor calculus.

Experimental Tests

General relativity has been confirmed by a number of empirical tests, including the precession of the orbit of Mercury, the deflection of light by gravity observed during solar eclipses, and the time dilation of clocks in gravitational fields measured by very precise atomic clocks. More recently, the detection of gravitational waves by the LIGO and Virgo observatories has provided direct evidence of the dynamic nature of spacetime.

Astrophysical Implications

General relativity has profound implications for astrophysics and cosmology. For example, it predicts the existence of black holes, regions of spacetime from which nothing, not even light, can escape. It also underpins our understanding of the Big Bang and the evolution of the universe, as well as the physics of neutron stars and the possibility of wormholes.

Challenges and Extensions

While general relativity has been enormously successful, it is not compatible with quantum mechanics, the other great physical theory of the 20th century. This incompatibility has led to ongoing efforts to develop a theory of quantum gravity, with candidates including string theory and loop quantum gravity. Additionally, the mysterious dark energy, which drives the accelerated expansion of the universe, and dark matter, which explains anomalous rotational speeds of galaxies, are both areas of active research and debate within the framework of general relativity.

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