Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics

TL;DR

This paper analyzes the causality and stability of relativistic viscous magneto-hydrodynamics, incorporating magnetic field effects into Israel-Stewart theory, and finds conditions under which the fluid remains stable and causal.

Contribution

It introduces a modified Israel-Stewart theory including magnetic effects and examines how magnetic fields influence causality and stability in relativistic viscous fluids.

Findings

Causality bounds are independent of magnetic field magnitude for bulk viscosity.

Modified IS theory reveals new non-hydrodynamic modes with preserved causality conditions.

Fluid remains stable and causal under certain asymptotic conditions despite magnetic influences.

Abstract

We investigate the causality and the stability of the relativistic viscous magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfv\'en and the magneto-sonic modes.In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfv\'en modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.