Gravitation without the equivalence principle

TL;DR

This paper demonstrates that the teleparallel gauge formulation of gravity remains consistent without relying on the equivalence principle, unlike the geometric approach of general relativity.

Contribution

It shows that teleparallel gravity, as a gauge theory for translations, does not require the equivalence principle to be a consistent description of gravitation.

Findings

Teleparallel gravity is a gauge theory for the translation group.

It remains consistent without the equivalence principle.

Geometric general relativity requires the equivalence principle.

Abstract

In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. On the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence.