A Rigorous Study of Hawking Radiation on Collapsing Charged Spherically Symmetric Spacetimes

TL;DR

This paper rigorously analyzes Hawking radiation in collapsing charged black holes, establishing decay rates and finiteness of emitted particles, with implications for extremal and non-extremal black hole models.

Contribution

It provides a rigorous mathematical framework for late-time Hawking radiation in charged black hole formation, including decay bounds and emission finiteness for extremal cases.

Findings

Decay rate of radiation approaches the late-time limit

Finiteness of total emitted massless bosons for extremal black holes

Established bounds on radiation emission rates

Abstract

In this paper, we give a rigorous mathematical treatment of the late time Hawking radiation of massless bosons emitted by a class of collapsing, spherically symmetric, charged models of black hole formation, including both extremal and sub-extremal black holes. We will also prove a bound on the rate at which the radiation emitted approaches this late time limit. This includes an integrable decay rate of radiation emitted by extremal black holes, for which the late time limit vanishes. Thus, we show that the total expected quantity of any massless boson emitted by an extremal \RNS black hole is finite.