Lie Algebra Expansions and Actions for Non-Relativistic Gravity

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.
Comment: 37 pages, 1 figure; v2: minor editing plus added references