Abstract
An approach to black hole quantization is proposed wherein it is assumed that quantum coherence is preserved. After giving our motivations for such a quantization procedure we formulate the background field approximation, in which particles are divided into `hard' particles and `soft' particles. The background spacetime metric depends both on the in-states and on the out-states. A consequence of our approach is that four-geometries describing gravitational collapse will show the same topological structure as flat Minkowski space. We present some model calculations and extensive discussions. In particular, we show, in the context of a toy model, that the S-matrix describing soft particles in the hard particle background of a collapsing star is unitary; nevertheless, part of the spectrum of particles is shown to be approximately thermal. We also conclude that there is an interesting topological (and signature) constraint on manifolds underlying conventional functional integrals.