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 omega = ...
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 omega = -kM/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. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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