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

Harald Schmid
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Abstract

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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Harald Schmid. 2002-07-26. Bound State Solutions of the Dirac Equation in the Extreme Kerr Geometry. https://doi.org/10.1002/mana.200410205

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