Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry

Details Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry

2002-07-26

arxiv.org/abs/math-ph/0207039v2

Physics

Mathematical Physics

17 pages, 3 figures, small corrections and improvements

Scientific paper

In this paper we consider bound state solutions, i.e., normalizable time-periodic solutions of the Dirac equation in the exterior region of an extreme Kerr black hole 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 $\omega = -\frac{kM}{2J}$. 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.

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