Relativistic dissipative magnetohydrodynamics from the Boltzmann equation for 2-particle species gas

Abstract

We derive the equations of motion of relativistic magnetohydrodynamics from the Boltzmann equation using the method of moments. We consider a locally electrically neutral system composed of two particle species with opposite charges, with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. We find that the dynamics of this fluid changes dramatically in the presence of a magnetic field. The shear stress tensor no longer adheres to a single differential equation; instead, it splits into three non-degenerate components, each evolving according to distinct dynamical equations. Exploring these equations in a Bjorken flow scenario, we find that for large magnetic fields, our theory predicts oscillatory behavior beyond the scope of an Israel-Stewart-like theory.