Symmetric hyperbolic systems for Bianchi equations

TL;DR

This paper develops a family of symmetric hyperbolic systems for the Bianchi equations, ensuring well-posedness with physically relevant characteristics, and introduces new positivity properties of the Bel tensor to establish hyperbolicity.

Contribution

It presents a novel formulation of the Bianchi equations as symmetric hyperbolic systems with physical characteristics, using new positivity properties of the Bel tensor.

Findings

Successfully constructs hyperbolic systems with light cone and timelike hypersurface characteristics.

Establishes new positivity properties of the Bel tensor for hyperbolicity proof.

Provides a framework for analyzing Bianchi equations in a hyperbolic setting.

Abstract

We obtain a family of first-order symmetric hyperbolic systems for the Bianchi equations. They have only physical characteristics: the light cone and timelike hypersurfaces. In the proof of the hyperbolicity, new positivity properties of the Bel tensor are used.