Difference between revisions of "Einstein equations"
From Encyclopedia of Mathematics
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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: | 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 | + | 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==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> L.D. Landau, E.M. Lifshitz, "The classical theory of fields" , Addison-Wesley (1962) (Translated from Russian)</TD></TR> | + | <table> |
| − | + | <TR><TD valign="top">[1]</TD> <TD valign="top"> L.D. Landau, E.M. Lifshitz, "The classical theory of fields" , Addison-Wesley (1962) (Translated from Russian)</TD></TR> | |
| − | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> S. Weinberg, "Gravitation and cosmology" , Wiley (1972) pp. Chapt. 7</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> R.M. Wald, "General relativity" , Univ. Chicago Press (1984) pp. Chapt. 4</TD></TR> | |
| − | + | </table> | |
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Latest revision as of 18:30, 4 May 2023
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=14498
Einstein equations. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Einstein_equations&oldid=14498
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article