Electromagnetic fire-hose instability in a fully relativistic bi-Maxwellian plasma

Detailed properties of the classical hydromagnetic Alfven wave and the fire-hose instability, driven by an excess in the parallel energy are well understood in the nonrelativistic regime. In this brief communication, the analysis is extended to the fully relativistic regime. The analysis is carried out for fully relativistic bi-Maxwellian distributions of electrons and ions (or positrons). It is shown that the relativistic effect has a nonnegligible effect on the wave and stability properties of the low-frequency modes under certain conditions.