  Understanding the end state of black hole evaporation, the microscopic origin
of black hole entropy, the information loss paradox, and the nature of the
singularity arising in gravitational collapse - these are outstanding
challenges for any candidate quantum theory of gravity. Recently, a
midisuperspace model of quantum gravitational collapse has been solved using a
lattice regularization scheme. It is shown that the mass of an eternal black
hole follows the Bekenstein spectrum, and a related argument provides a fairly
accurate estimate of the entropy. The solution also describes a quantized
mass-energy distribution around a central black hole, which in the WKB
approximation, is precisely Hawking radiation. The leading quantum
gravitational correction makes the spectrum non-thermal, thus providing a
plausible resolution of the information loss problem.
