# Covariant field equations in supergravity

## TL;DR

This paper proves that supergravity field equations can be made covariant modulo other equations, providing a systematic way to obtain covariant multiplets of equations, which simplifies their analysis.

## Contribution

It establishes the existence of covariant forms of supergravity field equations equivalent to the standard ones, facilitating their use in theoretical developments.

## Key findings

- Existence of covariant supergravity field equations.
- Method to systematically covariantize ordinary equations.
- Application to derive multiplets of field equations.

## Abstract

Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations.