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

F. Belgiorno and S. L. Cacciatori
Phys. Rev. D 79, 124024 – Published 16 June 2009

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-Nordström-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 nonexistence 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 the 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.

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  • Received 31 October 2008

DOI:https://doi.org/10.1103/PhysRevD.79.124024

©2009 American Physical Society

Authors & Affiliations

F. Belgiorno*

  • Dipartimento di Fisica, Università di Milano, 20133 Milano, Italy, and I.N.F.N., Sezione di Milano, Italy

S. L. Cacciatori

  • Dipartimento di Fisica e Matematica, Università dell’Insubria, 22100 Como, Italy, and I.N.F.N., Sezione di Milano, Italy

  • *belgiorno@mi.infn.it
  • sergio.cacciatori@uninsubria.it

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Vol. 79, Iss. 12 — 15 June 2009

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