Three-dimensional Newtonian gravity with cosmological constant and torsion

TL;DR

This paper introduces a novel three-dimensional Newtonian gravity model incorporating torsion and a cosmological constant, derived from a non-relativistic limit of an extended teleparallel algebra, and explores its infinite-dimensional extension.

Contribution

It presents the first teleparallel analogue of Newtonian gravity with torsion and extends it to an infinite-dimensional algebra using Lie algebra expansion.

Findings

Developed a non-relativistic limit of an extended teleparallel algebra with torsion.

Constructed an infinite-dimensional torsional Galilean gravity model.

Reproduces known Galilean gravity in the zero cosmological constant limit.

Abstract

In this paper we present an alternative cosmological extension of the three-dimensional extended Newtonian Chern-Simons gravity by switching on the torsion. The theory is obtained as a non-relativistic limit of an enhancement and $U(1)$-enlargement of the so-called teleparallel algebra and can be seen as the teleparallel analogue of the Newtonian gravity theory. The infinite-dimensional extension of our result is also explored through the Lie algebra expansion method. An infinite-dimensional torsional Galilean gravity model is presented which in the vanishing cosmological constant limit reproduces the infinite-dimensional extension of the Galilean gravity theory.