Ingoing Eddington-Finkelstein Metric of an Evaporating Black Hole

TL;DR

This paper derives an approximate, time-dependent ingoing Eddington-Finkelstein metric for an evaporating black hole, incorporating Hawking radiation effects as a first-order perturbation to Schwarzschild spacetime.

Contribution

It introduces a novel first-order perturbative metric for evaporating black holes that accounts for Hawking radiation in a realistic quantum state.

Findings

Provides a practical approximation for the evolving black hole metric.

Incorporates Hawking radiation back reaction in a linearized framework.

Enhances understanding of black hole evaporation dynamics.

Abstract

We present an approximate time-dependent metric in ingoing Eddington-Finkelstein coordinates for an evaporating nonrotating black hole as a first-order perturbation of the Schwarzschild metric, using the linearized back reaction from a realistic approximation to the stress-energy tensor for the Hawking radiation in the Unruh quantum state.