A geometric view on local Lorentz transformations in teleparallel gravity

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.

arXiv comment19 pages, no figures; contribution to the Special Issue of the International Journal of Geometric Methods in Modern Physics dedicated to the conference Geometric Foundations of Gravity in Tartu 2021

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Cited by in corpus (7)

• Teleparallel Gravity: From Theory to Cosmology
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
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• Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions
• Local symmetries in $f(T)$-like models: lessons from 2D