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

Abstract

AbstractIn 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)