Pair-production of charged Dirac particles on charged Nariai and ultracold black hole manifolds

TL;DR

This paper investigates the spontaneous discharge of charged black holes through pair-production of charged Dirac particles, using exact calculations on special black hole backgrounds and comparing different computational methods.

Contribution

It provides exact calculations of pair-production on specific charged black hole backgrounds and compares multiple analytical approaches, including zeta-function, transmission coefficient, and WKB methods.

Findings

Exact pair-production calculations on Nariai and ultracold black holes.

Comparison of zeta-function and transmission coefficient methods.

Analysis of thermal effects on black hole discharge.

Abstract

Spontaneous loss of charge by charged black holes by means of pair-creation of charged Dirac particles is considered. We provide three examples of exact calculations for the spontaneous discharge process for 4D charged black holes by considering the process on three special non-rotating de Sitter black hole backgrounds, which allow to bring back the problem to a Kaluza-Klein reduction. Both the zeta-function approach and the transmission coefficient approach are taken into account. A comparison between the two methods is also provided, as well as a comparison with WKB results. In the case of non-zero temperature of the geometric background, we also discuss thermal effects on the discharge process.