Isothermal Plasma Waves in Gravitomagnetic Planar Analogue

We investigate the wave properties of the Kerr black hole with isothermal plasma using 3+1 ADM formalism. The corresponding Fourier analyzed perturbed GRMHD equations are used to obtain the dispersion relations. These relations lead to the real values of the components of wave vector $\textbf{k}$ which are used to evaluate the quantities like phase and group velocities etc. These have been discussed graphically in the neighborhood of the pair production region. The results obtained verify the conclusion of Mackay et al. according to which rotation of a black hole is required for negative phase velocity propagation.