Saturday, 20 July 2013

Einstein's field Equations

The Einstein field equations (EFE) or Einstein's equations are a set of 10 equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of space time being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local space time curvature (expressed by the Einstein tensor) with the local energy and momentum within that space time (expressed by the stress–energy tensor).

This section contains words and symbol which need high level knowledge of physics to understand.

Tensors consist of more than the 3 element of dimensions that the normal vector represent. Hence a Sphere volume dimension can be described by a Tensor instead of a vector;
Space can be represented in multiple dimensions = The geometry of such representation is called a manifold which is an imaginary volume.

The condensed form of Einstein Field equation is as follows :

G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}

where Guv is the space curvature Tensor measured in unitsd of per meters
Tuv is the Stress energy Tensor measured in Kg/sec2, guv is the metric of space-time (how we measure distances in space-time), G is the gravitational constant having a value of G = 6.673 × 10-11 m3/kg•s2, c is the speed of light, i.e 2.99792458 x 108 m/s.

Derivation of such equation is beyond the scope of the website.

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