Breakdown of the semiclassical approximation at the black hole horizon.

The deenition of matter states on spacelike hypersurfaces of a 1+1 dimensional black hole spacetime is considered. The eeect of small quantum uctuations of the mass of the black hole due to the quantum nature of the infalling matter is taken into account. It is then shown that the usual approximation of treating the gravitational eld as a classical background on which matter is quantized, breaks down near the black hole horizon. Specii-cally, on any hypersurface that captures both infalling matter near the horizon and Hawking radiation, quantum uctuations in the background geometry become important, and a semi-classical calculation is inconsistent. An estimate of the size of correlations between the matter and gravity states shows that they are so strong that a uctuation in the black hole mass of order e ?M=MPlanck produces a macroscopic change in the matter state.