A geometric view on local Lorentz transformations in teleparallel gravity

TL;DR

This paper provides a geometric perspective on local Lorentz transformations in teleparallel gravity, clarifying different notions of invariance and offering a unified interpretation of the dynamical fields.

Contribution

It introduces a geometric interpretation that distinguishes various notions of Lorentz invariance in teleparallel gravity, refining existing conceptual frameworks.

Findings

Different notions of Lorentz invariance are clarified geometrically.

A unified interpretation of dynamical fields in teleparallel gravity is proposed.

The work distinguishes between invariance notions in different formulations.

Abstract

Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that modifications of general relativity in the teleparallel framework break a certain notion of local Lorentz invariance, which is present in the pure tetrad formulation of such theories, while another notion present in the covariant formulation is preserved. We illuminate these different notions from a geometric perspective, and distinguish them from what is commonly understood as breaking of local Lorentz invariance in the context of gravity phenomenology. Based on physical arguments, we present a geometric interpretation of the dynamical fields in teleparallel gravity, which unified and refines the conventional approaches.