Breakdown of the semiclassical approximation at the black hole horizon

TL;DR

This paper demonstrates that the semiclassical approximation fails near black hole horizons due to significant quantum fluctuations in the black hole mass, challenging the validity of treating gravity classically in such regions.

Contribution

It shows that quantum fluctuations of the black hole mass invalidate the semiclassical approximation at the horizon, revealing strong matter-gravity correlations.

Findings

Semiclassical approximation breaks down near the horizon.

Quantum fluctuations cause macroscopic changes in matter states.

Strong matter-gravity correlations are present at the horizon.

Abstract

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 infalling 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.