PROBLEM OF TIME AND QUANTUM BLACK-HOLES

We discuss the derivation of the so-called semiclassical equations for both minisuperspace and dilaton gravity. We find that there is no systematic derivation of a semiclassical theory in which quantum mechanics is formulated in a space-time that is a solution of Einstein's equations, with the expectation value of the matter stress tenser on the right-hand side. The issues involved are related to the well-known problems associated with the interpretation of the Wheeler-DeWitt equation in quantum gravity, including the problem of time. We explore the de Broglie-Bohm interpretation of quantum mechanics (and field theory) as a way of spontaneously breaking general covariance, and thereby give meaning to the equations that many authors have been using to analyze black hole evaporation. We comment on the implications for the ''information loss'' problem.