Quantization in black hole backgrounds

Quantum field theory in a semiclassical background can be derived as an approximation to quantum gravity from a weak-coupling expansion in the inverse Planck mass. Such an expansion is studied for evolution on nice slices in the spacetime describing a black hole of mass M. Arguments for a breakdown of this expansion are presented, due to significant gravitational coupling between fluctuations, which is consistent with the statement that existing calculations of information loss in black holes are not reliable. For a given fluctuation, the coupling to subsequent fluctuations becomes of order unity by a time of order M-3. Lack of a systematic derivation of the weakly coupled/semiclassical approximation would indicate a role for the nonperturbative dynamics of gravity, and possibly for the proposal that such dynamics has an essentially nonlocal quality.