On the Hawking radiation as tunneling for a class of dynamical black holes

TL;DR

This paper investigates Hawking radiation as tunneling in dynamical black holes, showing that surface gravity governs horizon instability and temperature in evolving black holes using Hamilton-Jacobi and Kodama-Hayward frameworks.

Contribution

It applies the Hamilton-Jacobi tunneling method to dynamical black holes, establishing a connection between surface gravity, horizon instability, and temperature in evolving spacetimes.

Findings

Surface gravity governs horizon singularity strength.

The tunneling method applies to black holes in expanding universes.

Temperature remains well-defined during slow evolution.

Abstract

The instability against emission of massless particles by the trapping horizon of an evolving black hole is analyzed with the use of the Hamilton-Jacobi method. The method automatically selects one special expression for the surface gravity of a changing horizon. Indeed, the strength of the horizon singularity turns out to be governed by the surface gravity as was defined a decade ago by Hayward using Kodama's theory of spherically symmetric gravitational fields. The theory also applies to point masses embedded in an expanding universe, were the surface gravity is still related to Kodama-Hayward theory. As a bonus of the tunneling method, we gain the insight that the surface gravity still defines a temperature parameter as long as the evolution is sufficiently slow that the black hole pass through a sequence of quasi-equilibrium states.