Due to their weak interactions with matter, neutrinos are free-streaming in most parts of the universe. Semi-transparent conditions for low energy neutrinos establish only where the matter density exceeds 10^10 g/cm^3. Self-gravitation limits the extent of these regions or induces a collapse to a compact object on a dynamical time scale. Neutrino transport is therefore often subject to the general relativistic effects of curved space-time in the vicinity of a compact object. As a Fermion, the neutrino carries energy and lepton number through the medium, leading to changes in temperature and electron abundance. Both are key quantities for the dynamics of matter during a supernova explosion. I discuss the gap between formal beauty and numerical implementation of general relativistic Boltzmann neutrino transport in spherical symmetry and review some approximations that have been successful in multi-dimensional supernova models.
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