Conservative General Relativistic Radiation Hydrodynamics in Spherical Symmetry and Comoving Coordinates

The description of general relativistic radiation hydrodynamics in spherical symmetry is presented in natural coordinate choices. For hydrodynamics, comoving coordinates are chosen, and the momentum phase space for the radiation particles is described in comoving frame four momenta. We also investigate a description of the momentum phase space in terms of particle impact parameter and energy at infinity and derive a simple approximation to the general relativistic Boltzmann equation. Further developed are, however, the exact equations in comoving coordinates, because the description of the interaction between matter and radiation particles is best described in the closely related orthonormal basis comoving with the fluid elements. We achieve a conservative and concise formulation of radiation hydrodynamics that is well suited for numerical implementation by a variety of methods. The contribution of radiation to the general relativistic jump conditions at shock fronts is discussed, and artificial viscosity is consistently included in the derivations in order to support approaches relying on this option.