Black Holes, Hawking Radiation and the Information Paradox

This talk is about results obtained by Kirill Melnikov and myself pertaining to the canonical quantization of a massless scalar field in the presence of a Schwarzschild black hole. After a brief summary of what we did and how we reproduce the familiar Hawking temperature and energy flux, I focus attention on how our discussion differs from other treatments. In particular I show that we can define a system which fakes an equilibrium thermodynamic object whose entropy is given by the $A/4$ (where $A$ is the area of the black hole horizon), but for which the assignment of a classical entropy to the system is incorrect. Finally I briefly discuss a discretized version of the theory which seems to indicate that things work in a surprising way near $r=0$.