On the evolution equations for ideal magnetohydrodynamics in curved spacetime

TL;DR

This paper develops a symmetric hyperbolic evolution system for the Einstein-Maxwell-Euler equations in curved spacetime, incorporating ideal magnetohydrodynamics using a tetrad formalism and Weyl tensor components.

Contribution

It introduces a novel first-order symmetric hyperbolic formulation for Einstein-Maxwell-Euler systems including ideal MHD in curved spacetime.

Findings

Constructed a hyperbolic evolution system ensuring well-posedness.

Incorporated Weyl tensor components as unknowns.

Included ideal magnetohydrodynamics as a special case.

Abstract

We examine the problem of the construction of a first order symmetric hyperbolic evolution system for the Einstein-Maxwell-Euler system. Our analysis is based on a 1+3 tetrad formalism which makes use of the components of the Weyl tensor as one of the unknowns. In order to ensure the symmetric hyperbolicity of the evolution equations implied by the Bianchi identity, we introduce a tensor of rank 3 corresponding to the covariant derivative of the Faraday tensor. Our analysis includes the case of a perfect fluid with infinite conductivity (ideal magnetohydrodynamics) as a particular subcase.