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We present an implicit finite difference representation for generalrelativistic radiation hydrodynamics in spherical symmetry. Our code,Agile-Boltztran, solves the Boltzmann transport equation for the angular andspectral neutrino distribution functions in self-consistent simulations ofstellar core collapse and postbounce evolution. It implements a dynamicallyadaptive grid in comoving coordinates. Most macroscopically interestingphysical quantities are defined by expectation values of the distributionfunction. We optimize the finite differencing of the microscopic transportequation for a consistent evolution of important expectation values. We testour code in simulations launched from progenitor stars with 13 solar masses and40 solar masses. ~0.5 s after core collapse and bounce, the protoneutron starin the latter case reaches its maximum mass and collapses further to form ablack hole. When the hydrostatic gravitational contraction sets in, we find atransient increase in electron flavor neutrino luminosities due to a change inthe accretion rate. The muon- and tauon-neutrino luminosities and rms energies,however, continue to rise because previously shock-heated material with anon-degenerate electron gas starts to replace the cool degenerate material attheir production site. We demonstrate this by supplementing the concept ofneutrinospheres with a more detailed statistical description of the origin ofescaping neutrinos. We compare the evolution of the 13 solar mass progenitorstar to simulations with the MGFLD approximation, based on a recently developedflux limiter. We find similar results in the postbounce phase and validate thisMGFLD approach for the spherically symmetric case with standard input physics.Comment: reformatted to 63 pages, 24 figures, to be published in ApJ

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Spacetime