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)], where we only considered the non-resistive limit, to the case of finite electric conductivity. This requires keeping terms proportional to the electric field $E^{\mu }$ 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.

11 pages

References in corpus (2)

• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Cosmology with inhomogeneous magnetic fields

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