Relativistic resistive dissipative magnetohydrodynamics from the relaxation time approximation
Ankit Kumar Panda, Ashutosh Dash, Rajesh Biswas, Victor Roy
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 [A. K. Panda et al., J. High Energy Phys. 03 (2021) 216] where we considered the nonresistive 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 second order, the new transport coefficients that couple electromagnetic fields with the dissipative quantities appear, which are different from those obtained in the 14-moment approximation [G. S. Denicol et al., Phys. Rev. D 99, 056017 (2019).] in the presence of the electromagnetic field. Also, we found the various components of conductivity in this case.