Relativistic radiation hydrodynamics: Mixed-frame tensor approach

Relativistic radiation hydrodynamics is needed to properly treat accretion flow with relativistic motion, with a strong radiation field, or under strong gravity, as well as other relativistic astrophysical phenomena. Simple and convenient relativistic radiation moment equations are derived from the tensor equations. Tensors and the interaction terms between radiation and matter are defined or evaluated either in a fixed frame or in a comoving frame. This mixed-frame tensor approach is easier to understand and apply to astrophysical problems. Detailed derivation of the equations is shown for a spherically symmetric case. Some interesting aspects of relativistic radiation hydrodynamics are also discussed.