Torsion in the Classical Spacetime Context

TL;DR

This paper explores how torsion can be incorporated into classical spacetime models, providing a new perspective on teleparallel gravity and its relation to Newton-Cartan theory.

Contribution

It introduces a method to embed torsion into classical spacetime, establishing a non-unique correspondence with Newton-Cartan models.

Findings

Established a classical theory of gravity with torsion and a closed temporal metric.

Proved a theorem relating Newton-Cartan models to torsional models.

Clarified the interpretation of torsional forces in classical spacetime.

Abstract

Teleparallel gravity, an empirically equivalent counterpart to General Relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the torsional forces of Teleparallel gravity, we consider a context in which forces are better understood: classical spacetimes. We propose a method of incorporating torsion into the classical spacetime context that yields a classical theory of gravity with a closed temporal metric and spacetime torsion. We then prove a result analogous to the Trautman degeometrization theorem, that every model of Newton-Cartan theory gives rise, non-uniquely, to a model of this theory.