A Quantum Model of Schwarzschild Black Hole Evaporation

TL;DR

This paper develops a quantum model for the evaporation process of Schwarzschild black holes, capturing the transition from thermal equilibrium to complete evaporation and analyzing the end-state geometry.

Contribution

It introduces a quantised Vaidya solution with a time-dependent quantum state to model black hole evaporation in a spherically symmetric setting.

Findings

Black hole shrinks to zero radius in finite proper time.

Hawking flux diverges at the evaporation endpoint.

End-state metric cannot be flat.

Abstract

We construct a one-loop effective metric describing the evaporation phase of a Schwarzschild black hole in a spherically symmetric null-dust model. This is achieved by quantising the Vaidya solution and by chosing a time dependent quantum state. This state describes a black hole which is initially in thermal equilibrium and then the equilibrium is switched off, so that the black hole starts to evaporate, shrinking to a zero radius in a finite proper time. The naked singularity appears, and the Hawking flux diverges at the end-point. However, a static metric can be imposed in the future of the end-point. Although this end-state metric cannot be determined within our construction, we show that it cannot be a flat metric.