  In this paper, the isothermal plasma wave properties in the neighborhood of
the pair production region for the Kerr black hole magnetosphere are discussed.
We have considered the Fourier analyzed form of the perturbed general
relativistic magnetohydrodynamical equations whose determinant leads to a
dispersion relation. For the special scenario, the $x$-component of the complex
wave vectors are numerically calculated. Respective components of the
propagation vector, attenuation vector, phase and group velocities are shown in
graphs. We have particularly investigated the existence of a Veselago medium
and wave behavior (modes of waves dispersion
