Hawking radiation and black hole gravitational back reaction - A quantum geometrodynamical simplified model

TL;DR

This paper presents a simplified quantum geometrodynamical model to analyze the back reaction of Hawking radiation on black hole evaporation, focusing on entropy as a measure of entanglement.

Contribution

It introduces a Schrödinger-like equation derived from Wheeler-DeWitt characteristics to study black hole and Hawking radiation evolution with back reaction effects.

Findings

Hawking radiation influences black hole quantum states

Entropy estimates indicate entanglement levels

Model captures key features of back reaction dynamics

Abstract

The purpose of this paper is to analyse the back reaction problem, between Hawking radiation and the black hole, in a simplified model for the black hole evaporation in the quantum geometrodynamics context. The idea is to transcribe the most important characteristics of the Wheeler-DeWitt equation into a Schr\"odinger's type of equation. Subsequently, we consider Hawking radiation and black hole quantum states evolution under the influence of a potential that includes back reaction. Finally, entropy is estimated as a measure of the entanglement between the black hole and Hawking radiation states in this model.