A geometric view on local Lorentz transformations in teleparallel gravity

Understand

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.