Relativistic Dissipative Magnetohydrodynamics for accretion disks

TL;DR

This work develops a relativistic magnetohydrodynamics framework for a dilute electron–ion plasma by solving the Boltzmann–Vlasov equation with the 14-moment (DNMR) approach, treating ions and electrons as a two-fluid system and including all components of the shear-stress tensor relative to the magnetic field. The model yields coupled evolution equations for the total and relative shear stresses that cannot be captured by standard Israel–Stewart-like theories, and it incorporates magnetic-field effects through the Faraday tensor and field-aligned stress coupling. In the linear regime and under strong magnetic fields, the analysis shows the firehose instability can arise when the longitudinal pressure (along the field) becomes sufficiently large, with transverse stress components becoming significant. The findings imply that transverse shear stresses may influence accretion-disk dynamics in extreme magnetization, suggesting revisions to standard accretion-disk RMHD formulations are warranted in strong-field regimes.

Abstract

We derive a relativistic magnetohydrodynamics (RMHD) theory for a dilute electron-ion gas governed by the Boltzmann-Vlasov equation, using the method of moments. This yields an extended MHD framework beyond standard astrophysical formulations, which typically include only the shear-stress component parllel to the magnetic field. We analyze our framework in the linear regime and show that it leads to the firehose instability when the bakground longitudinal pressure becomes large. In these extreme scenario, the transverse and semi-transverse shear-stress components become large and may play a role in accretion disk dynamics.