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 [1] 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 different values of these coefficients. We also derive the anisotropic transport coefficients in the Navier-Stokes limit.
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Panda, A.K., Dash, A., Biswas, R. et al. Relativistic non-resistive viscous magnetohydrodynamics from the kinetic theory: a relaxation time approach. J. High Energ. Phys. 2021, 216 (2021). https://doi.org/10.1007/JHEP03(2021)216
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DOI: https://doi.org/10.1007/JHEP03(2021)216