paper

Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions

arXiv:2305.06997 · doi:10.1142/S0219887824500464

Abstract

We study metric teleparallel geometries, which can either be defined through a Lorentzian metric and flat, metric-compatible affine connection, or a tetrad and a flat spin connection, which are invariant under the transitive action of a four-dimensional Lie group on their spatial equal-time hypersurfaces. There are three such group actions, and their corresponding spatial hypersurfaces belong to the Bianchi types II, III and IX, respectively. For each of these three symmetry groups, we determine the most general teleparallel geometry, and find that it is parametrized by six functions of time, one of which can be eliminated by the choice of the time coordinate. We further show that these geometries are unique up to global Lorentz transformations, coordinate transformations and changes of the choice of the parameter functions.

arXiv comment30 pages, no figures; contribution to the Special Issue on metric-affine gravity, Tartu, 2022, of the International Journal of Geometric Methods in Modern Physics

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