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General-relativistic radiation hydrodynamics and neutrino transport in polar-sliced space-time.

Extending the work of Schinder, Bludman, and Piran, I derive the equations of radiation hydrodynamics in polar-sliced space-time. The additional terms which describe the effects of neutrino stress energy on the gas dynamics are added to the equations of hydrodynamics. The neutrino Boltzmann equation and its lowest angular and energy moments are derived in comoving coordinates with neutrino energies and directions determined in comoving frames. It is shown that the Boltzmann equation gives the correct results when neutrinos are strongly trapped, and the neutrinos become just another component of a perfect gas. Techniques which I plan to use to numerically solve the neutrino transport equations are discussed.