The 3 + 1 Einstein equations (including a radiation component in the stress-energy tensor), the 3 + 1 equations for general relativistic hydrodynamics (including the radiation four-force density), and the 3 + 1 general relativistic Boltzmann equation, are all derived for time-dependent, spherically symmetric spacetimes. These equations are then specialized to maximally sliced spacetimes in the isotropic gauge. The implicit finite differencing of the Boltzmann equation and of the radiation contribution to the hydrodynamics equations is described, and a new implicit numerical scheme for the coupled collision term in the Boltzmann equation and the radiation four-force density in the hydrodynamics equations is presented. The results of a code test for this radiation code are given.
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Mezzacappa et al. (1989) studied this question.