  The 3+1 GRMHD equations for Schwarzschild spacetime in Rindler coordinates
with isothermal state of plasma are formulated. We consider the cases of
non-rotating and rotating backgrounds with non-magnetized and magnetized
plasmas. For these cases, the perturbed form of these equations are linearized
and Fourier analyzed by introducing plane wave type solutions. The determinant
of these equations in each case leads to two dispersion relations which give
value of the wave number $k$. Using the wave number, we obtain information like
phase and group velocities etc. which help to discuss the nature of the waves
and their characteristics. These provide interesting information about the
black hole magnetosphere near the horizon. There are cases of normal and
anomalous dispersion. We find a case of normal dispersion of waves when the
plasma admits the properties of Veselago medium. Our results agree with those
of Mackay et al. according to which rotation of a black hole is required for
negative phase velocity propagation.
