Lorentz gauge-invariant variables in torsion-based theories of gravity

TL;DR

This paper explores Lorentz gauge invariance in torsion-based gravity theories, demonstrating the physical equivalence of formulations with and without a spin-connection, which is crucial for understanding their consistency.

Contribution

It provides a proof that both spin-connection and non-spin-connection formulations of torsion-based gravity are physically equivalent, clarifying their gauge invariance.

Findings

Both formulations are physically equivalent.

Lorentz gauge invariance is maintained in both approaches.

The proof simplifies understanding of torsion-based gravity theories.

Abstract

General relativity dynamics can be derived from different actions -- which depart from the Einstein-Hilbert action in boundary terms -- and for different choices of the dynamical variables. Among them, the teleparallel equivalent of general relativity is a torsion-based theory for the tetrad field. More general torsion-based theories have been built in the last years, intending to supersede general relativity. There are two current ways to formulate such theories; one includes a spin-connection and the other does not. We discuss the notion of Lorentz gauge invariance in such theories, and give a simple but important proof that both formulations are physically equivalent.