Causality and stability of magnetohydrodynamics for an ultrarelativistic locally neutral two-component gas

We investigate the causality and stability of the relativistic theory of magnetohydrodynamics derived in [Phys. Rev. D 109, 096021 (2024)] to describe a locally neutral two-component plasma of massless particles. We show that this formalism is linearly causal and stable around global equilibrium, for any value of the magnetic field, and discuss its qualitative differences to the traditional Israel-Stewart formalism in the linear regime. Finally, we compare this framework with the magnetohydrodynamic model used in the study of astrophysical plasmas, in which only the longitudinal component of the shear-stress tensor is considered. We discuss the domain of applicability of this type of framework in the context of ultrarelativistic heavy-ion collisions.