Non-relativistic limit of the Mielke–Baekler gravity theory

Abstract

In this paper, we present a generalized 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 $$\left( p,q\right) $$ p , q parameters. In particular, torsionless models are recovered for $$q=0$$ q = 0 .