Gravitational Back Reaction of Hawking modes

TL;DR

This paper models black hole evaporation considering gravitational back reaction, showing that such effects can prevent complete evaporation and make the black hole effectively eternal.

Contribution

It introduces a toy model using Vaidya metric to incorporate back reaction, demonstrating how it alters the black hole evaporation process.

Findings

Back reaction suppresses evaporation rate significantly.

Singularity near the horizon is softened by back reaction.

Black hole can become effectively eternal due to back reaction.

Abstract

The radiation rate of an evaporating black hole is calculated in a toy model in which the geometry outside the collapsing matter is described by a Vaidya metric. When back reaction consistency is imposed, the singularity in the blueshift factor near the horizon is softened, suppressing the evaporation rate in the Schwarzschild case by the fourth power of the external time, thus rendering the hole eternal.