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

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.

Note:

17 pages, 3 figures, small corrections and improvements

Dirac equation: solution
black hole: Kerr
bound state
analytic properties
numerical calculations

References(12)

Figures(6)

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•
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