Relativistic resistive dissipative magnetohydrodynamics from the relaxation time approximation

TL;DR

This paper derives second-order relativistic resistive magnetohydrodynamic equations using the Boltzmann equation with the relaxation time approximation, revealing new electromagnetic coupling effects on dissipative processes.

Contribution

It extends previous non-resistive models by incorporating resistivity and electromagnetic coupling into second-order relativistic hydrodynamics.

Findings

Transport coefficients are independent of electromagnetic fields at first order.

Diffusion current depends on the electric field at first order.

New electromagnetic coupling coefficients appear at second order.

Abstract

Here we derive the relativistic resistive dissipative second-order magnetohydrodynamic evolution equations using the Boltzmann equation, thus extending our work from the previous paper \href{https://link.springer.com/article/10.1007/JHEP03(2021)216}{JHEP 03 (2021) 216} where we considered the non-resistive limit. We solve the Boltzmann equation for a system of particles and antiparticles using the relaxation time approximation and the Chapman-Enskog like gradient expansion for the off-equilibrium distribution function, truncating beyond second-order. In the first order, the bulk and shear stress are independent of the electromagnetic field, however, the diffusion current, shows a dependence on the electric field. In the first order, the transport coefficients~(shear and bulk stress) are shown to be independent of the electromagnetic field. The diffusion current, however, shows a dependence on the electric field. In the second-order, the new transport coefficients that couple electromagnetic field with the dissipative quantities appear, which are different from those obtained in the 14-moment approximation~\cite{Denicol:2019iyh} in the presence of the electromagnetic field. Also we found out the various components of conductivity in this case.