First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory

TL;DR

This paper derives a first-order 3+1 decomposition of the teleparallel equivalent of general relativity in the pure-tetrad formulation, showing it admits a symmetric hyperbolic structure similar to electrodynamics, aiding well-posedness.

Contribution

It provides the first-order reduction and hyperbolic formulation of TEGR in the pure-tetrad form, facilitating initial value problem analysis.

Findings

3+1 TEGR equations have principal part similar to tetrad GR reformulations

The equations admit a symmetric hyperbolic formulation

The structure resembles relativistic electrodynamics equations

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.