Well-posedness of the scale-invariant tetrad formulation of the vacuum Einstein equations

TL;DR

This paper demonstrates that a modified scale-invariant tetrad formulation of the vacuum Einstein equations is a well-posed mixed hyperbolic/parabolic system, ensuring the mathematical stability of the initial value problem.

Contribution

It introduces a small modification to Uggla et al's tetrad formulation, proving its well-posedness as a mixed hyperbolic/parabolic system.

Findings

The modified formulation is a mixed symmetric hyperbolic/parabolic system.

Well-posedness of the Cauchy problem is established.

The approach ensures mathematical stability of the Einstein equations in this formulation.

Abstract

We show that with a small modification, the formulation of the Einstein equations of Uggla et al, which uses tetrad variables normalised by the expansion, is a mixed symmetric hyperbolic/parabolic system. Well-posedness of the Cauchy problem follows from a standard theorem.