Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation

Abstract

We derive the equations of motion of relativistic, resistive, second-order dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation using the method of moments. We thus extend our previous work [Phys. Rev. D 98, 076009 (2018)PRVDAQ2470-001010.1103/PhysRevD.98.076009], where we only considered the nonresistive limit, to the case of finite electric conductivity. This requires keeping terms proportional to the electric field Eμ in the equations of motions and leads to new transport coefficients due to the coupling of the electric field to dissipative quantities. We also show that the Navier-Stokes limit of the charge-diffusion current corresponds to Ohm's law, while the coefficients of electrical conductivity and charge diffusion are related by a type of Wiedemann-Franz law.