Are General Relativity and Teleparallel Gravity Theoretically Equivalent?

Abstract

Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of space-time curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence and any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity.