Hyperbolicity of Divergence Cleaning and Vector Potential Formulations of GRMHD

Understand

We examine hyperbolicity of general relativistic magnetohydrodynamics with divergence cleaning, a flux-balance law form of the model not covered by our earlier analysis.

• The calculations rely again on a dual-frame approach, which allows us to effectively exploit the structure present in the principal part.
• We find, in contrast to the standard flux-balance law form of the equations, that this formulation is strongly hyperbolic, and thus admits a well-posed initial value problem.
• Formulations involving the vector potential as an evolved quantity are then considered.