The Teleparallel Equivalent of Newton-Cartan Gravity

TL;DR

This paper develops a teleparallel framework for Newton-Cartan theory, demonstrating its equivalence to Newtonian gravity and linking it with teleparallel gravity in general relativity through null reduction of a 5D gravitational wave solution.

Contribution

It introduces a teleparallelization of Newton-Cartan theory and establishes its consistency with teleparallel gravity in general relativity, connecting four fundamental theories.

Findings

Teleparallelization of Newton-Cartan theory yields Newtonian gravity.

Consistency established between teleparallel Newton-Cartan and general relativity.

Null reduction of 5D gravitational wave leads to teleparallel Newtonian gravity.

Abstract

We construct a notion of teleparallelization for Newton-Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton-Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity.