Equations of relativistic radiation hydrodynamics in spherical coordinates

The interaction between matter and radiation is one of the most important astrophysical processes, yet the proper treatment can be exceedingly difficult, especially when the flow is moving with relativistic velocity. Here, we derive relativistic radiation hydrodynamic equations from a covariant tensor formalism. The equations are applicable to a flow with an arbitrary geometry. Derivatives are expressed in the fixed frame while the interaction between the matter and the radiation is described by comoving quantities. This mixed-frame approach is easier to understand and apply to astrophysical problems than the previous comoving formalism. The hydrodynamic equations and the radiation moment equations are explicitly written down in spherical coordinates. A suitable form of the Eddington factor that closes the radiation moment equations is also discussed.