# nLab Einstein equation

### Context

#### Gravity

gravity, supergravity

# Contents

## Idea

What are called Einstein’s equations are the equations of motion of gravity: the Euler-Lagrange equations induced by the Einstein-Hilbert action.

They say that the Einstein tensor $G$ of the metric/the field of gravity equals the energy-momentum tensor $T$ of the remaing force- and matter-fields:

$G=T\phantom{\rule{thinmathspace}{0ex}}.$G = T \,.

## References

A general discssion is for instance in section 11 of

A discussion of the vacuum Einstein equations (only gravity, no other fields) in terms of synthetic differential geometry is in

Revised on January 6, 2013 06:27:27 by Urs Schreiber (89.204.139.89)