Namespaces
Variants
Actions

Einstein equations

From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

of the gravitational field

Fundamental equations in the general theory of relativity. They connect the metric tensor of the space-time continuum, which describes the gravitational field, and the physical characteristics of different forms of matter, described by means of the energy-momentum tensor:

$$R_{ik}-\frac12g_{ik}R=\frac{8\pi}{c^4}GT_{ik}.$$

Here $R_{ik}$ is the Ricci tensor, which can be expressed in terms of the metric tensor $g_{ik}$, $R=R_i^i$, $T_{ik}$ is the energy-momentum tensor, $c$ is the speed of light in vacuum, and $G$ is the gravitational constant.

References

[1] L.D. Landau, E.M. Lifshitz, "The classical theory of fields" , Addison-Wesley (1962) (Translated from Russian)
[a1] S. Weinberg, "Gravitation and cosmology" , Wiley (1972) pp. Chapt. 7
[a2] R.M. Wald, "General relativity" , Univ. Chicago Press (1984) pp. Chapt. 4
How to Cite This Entry:
Einstein equations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Einstein_equations&oldid=53932
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article