Symmetric Hyperbolic System in the Self-dual Teleparallel Gravity

TL;DR

This paper develops a symmetric hyperbolic system in self-dual teleparallel gravity, integrating the reality condition into the hyperbolicity framework, simplifying constraint equations, and facilitating initial value formulation for numerical relativity.

Contribution

It introduces a novel symmetric hyperbolic formulation of self-dual teleparallel gravity that includes the reality condition, simplifying the constraints compared to previous approaches.

Findings

The system is symmetric hyperbolic with the reality condition incorporated.

Constraint equations are simpler than in previous formulations.

Facilitates well-posed initial value problems in numerical relativity.

Abstract

In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity which is equivalent to the Ashtekar formulation is posed. This system is different from the ones in other works by that the reality condition of the spatial metric is included in the symmetric hyperbolicity and then is no longer an independent condition. In addition the constraint equations of this system are rather simpler than the ones in other works.