Breakdown of the semiclassical approximation at the black hole horizon

Esko Keski-Vakkuri, Gilad Lifschytz, Samir D. Mathur, Miguel Ortiz
1995 Physical Review D, Particles and fields  
The definition of matter states on spacelike hypersurfaces of a 1+1 dimensional black hole spacetime is considered. The effect of small quantum fluctuations 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 field as a classical background on which matter is quantized, breaks down near the black hole horizon. Specifically, on any hypersurface that captures both
more » ... g matter near the horizon and Hawking radiation, quantum fluctuations in the background geometry become important, and a semiclassical calculation is inconsistent. An estimate of the size of correlations between the matter and gravity states shows that they are so strong that a fluctuation in the black hole mass of order exp[-M/M_Planck] produces a macroscopic change in the matter state.
doi:10.1103/physrevd.51.1764 pmid:10018643 fatcat:yj7ep5p4krdk5grtglczkqzpfm