First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
Abstract
This paper presents a derivation of a first-order reduction and 3+1 decomposition of the teleparallel equivalent of general relativity (TEGR) in the pure-tetrad formulation (no spin connection). Our analysis demonstrates that in vacuum spacetimes, our 3+1 TEGR equations has the principal part of the differential operator equivalent to the one of tetrad reformulation of general relativity by Estabrook, Robinson, Wahlquist, and Buchman and Bardeen, and therefore the presented 3+1 decomposition of TEGR also admits a symmetric hyperbolic formulation, a desirable property for ensuring well-posedness of the initial value problem. Furthermore, the structure of the 3+1 equations possess a lot of similarities with the equations of relativistic electrodynamics and the recently proposed dGREM tetrad-reformulation of general relativity.
Keywords
Cite
@article{arxiv.2211.13659,
title = {First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory},
author = {Ilya Peshkov and Héctor Olivares and Evgeniy Romenski},
journal= {arXiv preprint arXiv:2211.13659},
year = {2025}
}
Comments
The accepted version for publication in Phys. Rev. D