An axisymmetric, stationary electrodynamic model of the central engine of an active galactic nucleus has been well formulated by Macdonald and Thorne. In this model the relativistic region around the central black hole must be filled by highly conducting plasma. We analyze plasma wave propagation in this region and discuss the results. We find that the ionosphere cannot exist right outside of the event horizon of the black hole. Another interesting aspect is that certain resonance phenomena can occur in this case.