Proper field quantization in black hole spacetimes

Canonical quantization of local field theories in classical black hole spacetimes with a single horizon leads to a particle number density with a thermal distribution in equilibrium at the Hawking temperature. A complete treatment including nonlocal quantum gravity effects has shown, however, that the full ''thermal vacuum'' of the theory is the false vacuum. In this work, we find the true vacuum consistent with the complete semiclassical analysis of quantum black holes. The theory is described by a ''microcanonical'' quantum field theory with fixed total energy E=M, the mass of the black hole. Considerations making use of the microcanonical density matrix as well as the idempotency condition show that particles in black hole backgrounds are described by pure states, unlike the canonical formulation. (C) 1995 Academic Press, Inc.