# Difference between revisions of "General Relativity"

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General relativity deals with spacetime and its behavior when an object has any behavior. It deals with things that the Special Theory of Relativity can not deal with. | General relativity deals with spacetime and its behavior when an object has any behavior. It deals with things that the Special Theory of Relativity can not deal with. | ||

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+ | == Concepts == | ||

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+ | In General Relativity, spacetime is a 4D differentiable [[manifold|Riemannian manifold]] whose curvature tensor satisfies Einstein’s field equations <cmath>R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}.</cmath> | ||

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+ | In this [[partial differential equation|system of PDEs]], <math>R_{\mu\nu}</math> is the [[Ricci curvature tensor]], and <math>R</math> is a summed version of the Ricci curvature tensor. The entire left hand side is sometimes known as the Einstein tensor for this reason. On the right-hand side, <math>T_{\mu\nu}</math> is the mass-energy tensor, which describes the distribution of [[mass-energy]] throughout the [[universe]], and the constant <math>\frac{8\pi G}{c^4}</math> is chosen so that General Relativity reduces to [[Classical Mechanics|Newtonian mechanics]] in the low-mass, low-velocity limit. | ||

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+ | == Predictions == | ||

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+ | Successful predictions of General Relativity include: | ||

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+ | *Gravitational lensing | ||

+ | *[[Black hole|Black holes]] | ||

+ | *Gravitational time dilation | ||

+ | *The precession of Mercury’s orbit | ||

== See Also == | == See Also == |

## Latest revision as of 01:49, 20 November 2020

General relativity deals with spacetime and its behavior when an object has any behavior. It deals with things that the Special Theory of Relativity can not deal with.

## Concepts

In General Relativity, spacetime is a 4D differentiable Riemannian manifold whose curvature tensor satisfies Einstein’s field equations

In this system of PDEs, is the Ricci curvature tensor, and is a summed version of the Ricci curvature tensor. The entire left hand side is sometimes known as the Einstein tensor for this reason. On the right-hand side, is the mass-energy tensor, which describes the distribution of mass-energy throughout the universe, and the constant is chosen so that General Relativity reduces to Newtonian mechanics in the low-mass, low-velocity limit.

## Predictions

Successful predictions of General Relativity include:

- Gravitational lensing
- Black holes
- Gravitational time dilation
- The precession of Mercury’s orbit

## See Also

*This article is a stub. Help us out by expanding it.*