  Equations of fully general relativistic radiation hydrodynamics in Kerr
space-time are derived. While the interactions between matter and radiation are
introduced in the comoving frame, the derivatives used when describing the
global evolutions of both the matter and the radiation are given in the
Boyer-Lindquist frame (BLF) which is a frame fixed to the coordinate describing
the central black hole. Around a rotating black hole, both the matter and the
radiation are influenced by the frame-dragging effects due to the black hole's
rotation. As a fixed frame, we use the locally non-rotating reference frame
(LNRF) which is one of the orthonormal frame. While the special relativistic
effects such as beaming effects are introduced by the Lorentz transformation
connecting the comoving frame and the LNRF, the general relativistic effects
such as frame-dragging and gravitational redshift are introduced by the tetrads
connecting the LNRF and the BLF.
