Torsion in the Classical Spacetime Context

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.