Massive Dirac particles on the background of charged de-Sitter black hole manifolds

TL;DR

This paper investigates massive Dirac fields around charged de-Sitter black holes, demonstrating the non-existence of bound states and exploring quantum discharge mechanisms through level-crossing analysis and WKB calculations.

Contribution

It provides a comprehensive analysis of Dirac fields on various charged de-Sitter black hole backgrounds, revealing the absence of bound states and examining quantum discharge processes.

Findings

No bound states for Dirac fields in all considered geometries.

Level-crossing indicates potential quantum instability and black hole discharge.

Calculated transmission coefficients for discharge in Nariai and ultracold geometries.

Abstract

We consider the behavior of massive Dirac fields on the background of a charged de-Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordstr\"{o}m-de-Sitter one, the Nariai case and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the non-existence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and it is shown to hold true even for extremal cases. Furthermore, we shift our attention on the very interesting problem of the quantum discharge of the black holes. Following Damour-Deruelle-Ruffini approach, we show that the existence of level-crossing between positive and negative continuous energy states is a signal of the quantum instability leading to the discharge of the black hole, and in the cases of the Nariai geometry and of the ultracold geometries we also calculate in WKB approximation the transmission coefficient related to the discharge process.