Well Posed Reduced Systems for the Einstein Equations

TL;DR

This paper reviews well-posed formulations of the Einstein equations' evolution problem in General Relativity, introducing a new hyperbolic system based on the Riemann tensor and Bianchi identities that includes matter sources.

Contribution

It presents a new first order symmetric hyperbolic system directly based on the Riemann tensor and Bianchi identities, with physical characteristics and matter sources, fully equivalent to previous formulations.

Findings

Developed a new hyperbolic system with physical characteristics

Included matter sources in the hyperbolic formulation

Established equivalence with existing formulations

Abstract

We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.