Quantum Fluctuations of Black Hole Geometry

TL;DR

This paper investigates the quantum nature of black hole horizons using a minisuperspace model, revealing quantum fluctuations that can cause the apparent horizon to separate from the event horizon, thus providing insights into black hole quantum mechanics.

Contribution

It introduces a quantum framework for black hole interior geometry, solving the Wheeler-DeWitt equation to define horizon properties quantum mechanically, and explores horizon fluctuations beyond classical trajectories.

Findings

Quantum fluctuations cause the apparent horizon to separate from the event horizon.

Wave functions transition from classical WKB solutions to tunneling solutions.

The model predicts a static black hole state with horizon separation due to quantum effects.

Abstract

By using the minisuperspace model for the interior metric ofstatic black holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and the expansions of null rays as quantum operators. Then, the exact wave function is found as a mass eigenstate, and the radius of the apparent horizon is quantum-mechanically defined. In the evolution of the metric variables, the wave function changes from a WKB solution giving the classical trajectories to a tunneling solution. By virtue of the quantum fluctuations of the metric evolution beyond the WKB approximation, we can observe a static black hole state with the apparent horizon separating from the event horizon.