Quantum gravity effects at a black hole horizon

TL;DR

This paper investigates how quantum fluctuations near a black hole horizon influence matter propagation, leading to significant energy-momentum fluctuations and potential modifications of the classical spacetime as perceived by outside observers.

Contribution

It introduces a model of quantum fluctuations affecting matter near the horizon and constructs an operator linking different entangled states, highlighting the role of a stretched horizon.

Findings

Energy-momentum fluctuations are large near the horizon.

Quantum effects can drastically alter the background spacetime.

Interactions between infalling matter and Hawking radiation are significant.

Abstract

Quantum fluctuations in the background geometry of a black hole are shown to affect the propagation of matter states falling into the black hole in a foliation that corresponds to observations purely outside the horizon. A state that starts as a Minkowski vacuum at past null infinity gets entangled with the gravity sector, so that close to the horizon it can be represented by a statistical ensemble of orthogonal states. We construct an operator connecting the different states and comment on the possible physical meaning of the above construction. The induced energy-momentum tensor of these states is computed in the neighbourhood of the horizon, and it is found that energy-momentum fluctuations become large in the region where the bulk of the Hawking radiation is produced. The background spacetime as seen by an outside observer may be drastically altered in this region, and an outside observer should see significant interactions between the infalling matter and the outgoing Hawking radiation. The boundary of the region of strong quantum gravitational effects is given by a time-like hypersurface of constant Schwarzschild radius $r$ one Planck unit away from the horizon. This boundary hypersurface is an example of a stretched horizon.