Hawking Radiation of a Quantum Black Hole in an Inflationary Universe

TL;DR

This paper investigates how cosmological inflation influences black hole evaporation through Hawking radiation in a two-dimensional Vaidya-de Sitter model, revealing conditions under which inflation suppresses or enhances evaporation.

Contribution

It introduces a method to compute Hawking radiation in dynamical black hole models with arbitrary mass functions and analyzes the impact of inflationary expansion on black hole evaporation.

Findings

Inflation tends to suppress black hole evaporation.

Large cosmological constant can increase evaporation.

Divergent outgoing radiation flux occurs at the Cauchy horizon.

Abstract

The quantum stress-energy tensor of a massless scalar field propagating in the two-dimensional Vaidya-de Sitter metric, which describes a classical model spacetime for a dynamical evaporating black hole in an inflationary universe, is analyzed. We present a possible way to obtain the Hawking radiation terms for the model with arbitrary functions of mass. It is used to see how the expansion of universe will affect the dynamical process of black hole evaporation. The results show that the cosmological inflation has an inclination to depress the black hole evaporation. However, if the cosmological constant is sufficiently large then the back-reaction effect has the inclination to increase the black hole evaporation. We also present a simple method to show that it will always produce a divergent flux of outgoing radiation along the Cauchy horizon where the curvature is a finite value. This means that the Hawking radiation will be very large in there and shall modify the classical spacetime drastically. Therefore the black hole evaporation cannot be discussed self-consistently on the classical Vaidya-type spacetime. Our method can also be applied to analyze the quantum stress-energy tensor in the more general Vaidya-type spacetimes.