Non-relativistic limit of the Mielke-Baekler gravity theory

TL;DR

This paper develops a comprehensive non-relativistic and Newtonian gravity model in three dimensions from the Mielke-Baekler theory, revealing how different known theories emerge by tuning parameters.

Contribution

It introduces the most general non-relativistic Chern-Simons gravity model and extends it to a Newtonian version, unifying various gravity theories through parameter choices.

Findings

Derivation of a non-relativistic gravity model with torsion and curvature parameters.

Construction of a Newtonian gravity theory from an enlarged algebra.

Recovery of torsionless models by setting specific parameters.

Abstract

In this paper, we present the most general non-relativistic Chern-Simons gravity model in three spacetime dimensions. We first study the non-relativistic limit of the Mielke-Baekler gravity through a contraction process. The resulting non-relativistic theory contains a source for the spatial component of the torsion and the curvature measured in terms of two parameters, denoted by $p$ and $q$. We then extend our results by defining a Newtonian version of the Mielke-Baekler gravity theory, based on a Newtonian like algebra which is obtained from the non-relativistic limit of an enhanced and enlarged relativistic algebra. Remarkably, in both cases, different known non-relativistic and Newtonian gravity theories can be derived by fixing the $\left(p,q\right)$ parameters. In particular, torsionless models are recovered for $q=0$.