Quantum gravitational collapse

We have outlined a canonical quantization of the LeMaitre-Tolman-Bondi models, which describe the collapse of inhomogeneous, non-rotating dust. Although, there are many models of gravitational collapse, this particular class of models stands out for its simplicity and the fact that both black holes and naked singularity end states may be realized on the classical level, depending on the initial conditions. We have solved the Wheeler-DeWitt equation exactly after regularization on a spatial lattice, and discussed some consequences of the quantization. The solutions describe Hawking radiation and provide an elegant microcanonical description of black hole entropy, but they also raise some very interesting questions concerning the nature of gravity's fundamental degrees of freedom.