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On the evolution equations for ideal magnetohydrodynamics in curved spacetime. (English) Zbl 1253.83011
Summary: 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.

MSC:
83C22 Einstein-Maxwell equations
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
76E20 Stability and instability of geophysical and astrophysical flows
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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