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Bound state solutions of the Dirac equation in the extreme Kerr geometry

✍ Scribed by Harald Schmid

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 309 KB
Volume: 274-275
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410205

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✦ Synopsis

Abstract

In this paper we consider bound state solutions, i.e., normalizable time‐periodic solutions of the Dirac equation in an extreme Kerr black hole background with mass M and angular momentum J. It is shown that for each azimuthal quantum number k and for particular values of J the Dirac equation has a bound state solution, and that the energy of this Dirac particle is uniquely determined by $ \textstyle \omega = { {kM} \over {2J} } $. Moreover, we prove a necessary and sufficient condition for the existence of bound states in the extreme Kerr‐Newman geometry, and we give an explicit expression for the radial eigenfunctions in terms of Laguerre polynomials. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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