  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.
