Cartan-like formulation of electric Carrollian gravity

TL;DR

This paper introduces a Cartan-like first-order action for electric Carrollian gravity, demonstrating its invariance under the Carroll group and deriving it from a limit of Einstein-Cartan theory, connecting various formulations.

Contribution

It provides a novel Cartan-like action principle for electric Carrollian gravity and links it to Einstein-Cartan theory through a smooth limit.

Findings

The action is invariant under the local Carroll group.

The first-order action can be obtained from a Carrollian limit of Einstein-Cartan gravity.

Connections with Hamiltonian and metric formulations are discussed.

Abstract

We present a Cartan-like first-order action principle for electric Carrollian gravity. The action is invariant under the local homogeneous Carroll group, albeit in a different representation than the one obtained by gauging the Carroll algebra. Additionally, we show that this first-order action can be derived from a smooth Carrollian limit of the Einstein-Cartan action. The connection with the Hamiltonian and metric forms of the action for electric Carrollian gravity, as well as with previous works in the literature, is also discussed.