# Einstein equations

From Encyclopedia of Mathematics

*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