Gravito-magnetic instabilities of Relativistic Magnetohydrodynamics

TL;DR

This paper investigates how relativistic effects influence gravito-magnetic instabilities in magnetized media, revealing that relativistic corrections tend to destabilize the system and providing stability criteria in different relativistic regimes.

Contribution

It provides a gauge-invariant analysis of gravito-magnetic instabilities in relativistic MHD with post-Newtonian and special relativistic frameworks, including stability criteria and wave velocities.

Findings

Relativistic effects tend to destabilize the medium.

PN corrections lower the critical Jeans wavelength.

Stability criteria are derived for both PN and SR MHD regimes.

Abstract

We study gravito-magnetic instabilities of a static homogeneous medium with an aligned magnetic field in the two contexts of relativistic magnetohydrodynamics (MHD): first, MHD with post-Newtonian (PN) corrections, and second, special relativistic (SR) MHD with weak gravity. The analysis in the PN MHD is made without taking the temporal gauge condition, thus results are gauge-invariant. The PN corrections of the internal energy, pressure, sound velocity and the Alfv\'en velocity lower the critical (Jeans) wavelength. {All relativistic effects tend to destabilize the system.} Although the SR MHD with weak gravity is presented in the harmonic gauge, in the presence of gravity the stability analysis is strictly valid to Newtonian order. In the absence of gravity, the SR MHD is independent of the gauge condition. We present the plane wave velocities and the stability criteria in both cases.