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Non-Existence of Time-Periodic Solutions of the Dirac Equation in an Axisymmetric Black Hole Geometry

Authors
  • Finster, F
  • Kamran, N
  • Smoller, J A
  • Yau, S T
Publication Date
Jan 01, 2000
Identifiers
DOI: 10.1002/(SICI)1097-0312(200007)53:7<902::AID-CPA4>3.0.CO;2-4
OAI: oai:cds.cern.ch:387539
Source
CERN Document Server
Keywords
Language
English
License
Unknown
External links

Abstract

We prove that, in the non-extreme Kerr-Newman black hole geometry, the Dirac equation has no normalizable, time-periodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar non-existence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast with the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity.

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