Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory:a relaxation time approach

TL;DR

This paper derives second-order relativistic viscous magnetohydrodynamic equations considering magnetic field effects using kinetic theory and relaxation time approximation, revealing new transport coefficients and their behavior in different magnetic field regimes.

Contribution

It introduces a novel derivation of relativistic viscous MHD equations with magnetic coupling, extending previous 14-moment approximation results using Chapman-Enskog expansion.

Findings

New second-order transport coefficients coupling magnetic field and dissipative quantities.

In weak magnetic field limit, equations match 14-moment approximation with different coefficients.

Derived anisotropic transport coefficients in the Navier-Stokes limit.

Abstract

We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in the 14-moment approximation \cite{Denicol:2018rbw} in the presence of a magnetic field. However, in the limit of the weak magnetic field, the form of these equations are identical to the 14-moment approximation albeit with a different values of these coefficients. We also derive the anisotropic transport coefficients in the Navier-Stokes limit.