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

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.