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 == | ||
| − | [Albert Einstein] | + | [[Albert Einstein]] |
| + | |||
| + | [[Physics]] | ||
{{stub}} | {{stub}} | ||
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 ![\[R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu}.\]](http://latex.artofproblemsolving.com/0/5/2/052236848e59f53926ee459416985f83238157fd.png)
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
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