GENERAL RELATIVISTIC RADIATION HYDRODYNAMICS: FREQUENCY-INTEGRATED RADIATION MOMENT FORMALISM

GENERAL RELATIVISTIC RADIATION HYDRODYNAMICS: FREQUENCY-INTEGRATED RADIATION MOMENT FORMALISM

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.