# Lie Algebra Expansions and Actions for Non-Relativistic Gravity

## TL;DR

This paper demonstrates how Lie algebra expansion methods can systematically derive algebras and actions for non-relativistic and ultra-relativistic gravity theories, unifying various recent approaches.

## Contribution

It introduces a general Lie algebra expansion technique applicable to constructing non-relativistic and Carroll gravity actions, extending previous methods.

## Key findings

- Successfully reconstructs known non-relativistic gravity algebras
- Provides explicit examples illustrating the method
- Suggests potential for extending to supergravity

## Abstract

We show that the general method of Lie algebra expansions can be applied to re-construct several algebras and related actions for non-relativistic gravity that have occurred in the recent literature. We explain the method and illustrate its applications by giving several explicit examples. The method can be generalized to include the construction of actions for ultra-relativistic gravity, i.e. Carroll gravity, and non-relativistic supergravity as well.