Einstein field equations

2016-09-13T07:34:46Z

49.205.9.73: /* Mathematical Interpretation */

{{complex|date=April 2012}}
{{General relativity}}

The '''Einstein field equations''', or '''Einstein-Hilbert equations''', or simply '''Einstein equations''' are [[equation]]s that describe [[gravity]] in the classical sense. They are named after [[Albert Einstein]] and [[David Hilbert]]. The basic idea is to use [[geometry]] to model the effects of gravity. The usual form of the equations is that of nonlinear [[partial differential equation]]s. Such equations are usually solved by [[approximation]]. An exact solution can be obtained in special cases, where certain assumptions are dropped, or simplified.

== Mathematical Interpretation ==
Einstein used mathematical objects called ''tensors'' to describe the curvature of [[spacetime]] to define [[gravity]]. The equation below is the general form of the EFE :

<math>R_{\mu\nu}-{1 \over 2}g_{\mu\nu},R+g_{\mu\nu}\Lambda={8\pi G \over c^4}T_{\mu\nu}</math>

Where Rμv is known as the ''Ricci curvature tensor'', gμv is the ''metric tensor'', ''R'' is the scalar curvature, Λ is the ''cosmological constant'', ''G'' is the [[gravitational constant]], [[π]] is [[pi]], [[c]] is the [[speed of light]], and Tμv is called the ''stress-energy tensor''.

{{science-stub}}

[[Category:Mathematics]]

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Einstein field equations