On the evolution equations for ideal magnetohydrodynamics in curved spacetime
Abstract
We examine the problem of the construction of a first order symmetric hyperbolic evolution system for the EinsteinMaxwellEuler 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.
 Publication:

General Relativity and Gravitation
 Pub Date:
 November 2012
 DOI:
 10.1007/s1071401214246
 arXiv:
 arXiv:1112.1525
 Bibcode:
 2012GReGr..44.2785P
 Keywords:

 Magnetohydrodynamics;
 Initial value problem;
 First order symmetric;
 Hyperbolic evolution system;
 Frame formulations;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 Mathematical Physics
 EPrint:
 25 pages, no figures. New references added. Comments added in the Introduction. Accepted for publication in General Relativity and Gravitation