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.

Concepts

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

In this system of PDEs, $R_{\mu\nu}$ is the Ricci curvature tensor, and $R$ 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, $T_{\mu\nu}$ is the mass-energy tensor, which describes the distribution of mass-energy throughout the universe, and the constant $\frac{8\pi G}{c^4}$ 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

Albert Einstein

Physics

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