Are General Relativity and Teleparallel Gravity Theoretically Equivalent?

TL;DR

This paper critically examines the claimed equivalence between general relativity and teleparallel gravity, arguing that they are not categorically equivalent and that teleparallel gravity contains more structural assumptions.

Contribution

It challenges the common view of equivalence between the two theories by applying categorical criteria and demonstrating that teleparallel gravity has strictly more structure.

Findings

Teleparallel gravity is not categorically equivalent to general relativity.

Teleparallel gravity posits more structure than general relativity.

Theories differ in their foundational geometric assumptions.

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.