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

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.

20 pages, 1 figure

References in corpus (8)

• The Chiral Magnetic Effect
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Lorentz Invariance in Chiral Kinetic Theory
• Electrical conductivity and charge diffusion in thermal QCD from the lattice
• Numerical magneto-hydrodynamics for relativistic nuclear collisions
• Stability and Causality in relativistic dissipative hydrodynamics
• Stable and causal relativistic Navier-Stokes equations
• Anomalous magnetohydrodynamics with longitudinal boost invariance and chiral magnetic effect