Magnetic Carrollian gravity from the Carroll algebra

TL;DR

This paper demonstrates the equivalence between the magnetic Carrollian limit of Einstein gravity and a Carrollian gravity theory derived from Carroll algebra gauging, clarifying their conceptual connection.

Contribution

It explicitly establishes the equivalence between the magnetic Carrollian limit of Einstein gravity and Carrollian gravity from Carroll algebra gauging.

Findings

Proves the equivalence between two formulations of Carrollian gravity.

Clarifies the relationship between Hamiltonian and algebraic approaches.

Provides a foundation for further studies in Carrollian gravitational theories.

Abstract

We explicitly establish the equivalence between the magnetic Carrollian limit of Einstein gravity defined through the Hamiltonian formalism and the Carrollian theory of gravity defined through a gauging of the Carroll algebra along the lines of standard Poincar\'e (or (A)dS) gaugings.