# Stringy (Galilei) Newton-Hooke Chern-Simons Gravities

## TL;DR

This paper constructs Chern-Simons gravity theories in 2+1 dimensions based on Stringy Galilei and Newton-Hooke algebras, exploring their invariant forms and resulting field equations, revealing novel features of non-relativistic gravity models.

## Contribution

It introduces new Chern-Simons gravity models using Stringy Galilei and Newton-Hooke algebras, analyzing their invariant structures and field equations, which differ from standard gravity theories.

## Key findings

- Existence of invariant non-degenerate bilinear form in some cases
- Field equations do not allow expressing spin connections in terms of dreibeins in certain cases
- Stringy Newton-Hooke algebra yields an invariant metric and expressible spin connections

## Abstract

We construct Chern-Simons gravities in $(2+1)$-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions. In the first case, there is an invariant and non-degenerate bilinear form, however, the field equations do not allow to express the spin connections in terms of the dreibeins. In the second case, there is no invariant non-degenerate bilinear form. Therefore, in both cases, we do not have an ordinary gravity theory. Instead, if we consider the stringy Newton-Hooke algebra with extensions as gauge group we have an invariant non-degenerate metric and from the field equations, we express the spin connections in terms of the geometric fields.