# nLab first-order formulation of gravity

### Context

#### Gravity

gravity, supergravity

# Contents

## Idea

The action functional of gravity was originally conceived as a functional on the space of pseudo-Riemannian metrics of a manifold $X$. Later on it was realized that it may alternatively naturally be thought of as a functional on the space of connections with values in the Poincare Lie algebra – essentially the Levi-Civita connection. This is known as the first order formalism or the Palatini formalism. The field strength of gravity – the Riemann tensor – is the curvature of Levi-Civita connection. Typically this is referred to a spin connection in this context.

The first order formalism is also the formalism in which supergravity has to be formulated.

## References

A decent introduction is in sections 4 and 5 of

A detailed account is in section I.4.1 of

Revised on May 22, 2013 14:57:27 by Urs Schreiber (84.153.217.239)