Radiation hydrodynamics in Kerr space-time: equations without coordinate singularity at the event horizon

Equations of fully general relativistic radiation hydrodynamics around a rotating black hole are derived by using the Kerr-Schild coordinate where there is no coordinate singularity at the event horizon. Since the radiation interacts with matter moving with relativistic velocities near the event horizon, the interplay between the radiation and the matter should be described fully relativistically. In the formalism used in this study, while the interactions between matter and radiation are introduced in the comoving frame, the equations and the derivatives for the description of the global evolution of both the matter and the radiation are given in the Kerr-Schild frame which is a frame fixed to the coordinate describing the central black hole. As a frame fixed to the coordinate, we use the locally non-rotating reference frame representing a radially falling frame when the Kerr-Schild coordinate is used. Around the rotating black hole, both the matter and the radiation are affected by the frame-dragging effects.