Influence of a plasma on the observational signature of a high-spin Kerr black hole

To approach a more reliable observational signature of a high-spin Kerr black hole, one should take into account the effects of its surroundings. To this end we study in this paper the influence of a surrounding plasma. We consider its refractive and dispersive effects on photon trajectories and ignore the gravitational effects of plasma particles as well as the absorption or scattering processes of photons. With two specific plasma models, we obtain analytical formulae for the black hole shadow and for the observational quantities of an orbiting "hot spot" seen by an observer located far away from the black hole. We find that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow and on the image position and redshift of the hot spot. These results may be tested by the Event Horizon Telescope in the future.