First-order hyperbolic formulation of the teleparallel gravity theory

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 have 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 possesses a lot of similarities with the equations of relativistic electrodynamics and the recently proposed dGREM tetrad-reformulation of general relativity.