Teleparallel Newton--Cartan gravity

TL;DR

This paper introduces a teleparallel formulation of Newton--Cartan gravity, derived as a large-speed-of-light limit of TEGR, offering a geometric perspective on Newtonian gravity within teleparallel frameworks.

Contribution

It presents a novel teleparallel approach to Newton--Cartan gravity, connecting it to TEGR and providing a new geometric formulation of the Newtonian limit.

Findings

Derived a teleparallel version of Newton--Cartan gravity from TEGR.

Showed how to recover standard Newtonian gravity via gauge fixing.

Established a geometric interpretation of Newtonian gravity in teleparallel terms.

Abstract

We discuss a teleparallel version of Newton--Cartan gravity. This theory arises as a formal large-speed-of-light limit of the teleparallel equivalent of general relativity (TEGR). Thus, it provides a geometric formulation of the Newtonian limit of TEGR, similar to standard Newton--Cartan gravity being the Newtonian limit of general relativity. We show how by a certain gauge-fixing the standard formulation of Newtonian gravity can be recovered.