I present here one approach to general relativistic radiation hydrodynamics. It is based on covariant tensor conservation equations and considers only the frequency-integrated total energy and momentum exchange between matter and the radiation field. It is also a mixed-frame formalism in the sense that, the interaction between radiation and matter is described with quantities in the comoving frame in which the interaction is often symmetric in angle while the radiation energy and momentum equations are expressed in the fixed frame quantities in which the derivatives are simpler. Hence, this approach is intuitive enough to be applied straightforwardly to any spacetime or coordinate. A few examples are provided along with caveats in this formalism.

Radiation hydrodynamics in high. velocity or high optical-depth flow should be treated under rigorous relativistic formalism. Relativistic radiation hydrodynamic moment equations are summarized, and its application to the near-critical accretion onto neutron star is discussed. The relativistic effects can dominate the dynamics of the flow even when the gravity is weak and the velocity is small. First order equations fail to describe the intricate relativistic effects correctly.

To examine the structure and dynamics of thick accretion disks, we use a two-dimensional viscous hydrodynamic code coupled with radiation transport. The α-model and the full viscous stress-tensor description for the kinematic viscosity are used. The radiation transport is treated in the gray, flux-limited diffusion approximation. The finite difference methods used are based on an explicit-implicit method. We apply the numerical code to the Super-Eddington black-hole model for SS 433.@The result for a very small viscosity parameter a reproduces well the characteristic features of SS 433, such as the relativistic jets with ~0.26c, the small collimation degree of the jets, the mass-outflow rate of ≥ 5 × 10 -7 M⊙yr-1, and the formation of the X-ray iron emission lines.