On the bound states of the Dirac equation in the extreme Kerr metric

Details On the bound states of the Dirac equation in the extreme Kerr metric On the bound states of the Dirac equation in the extreme Kerr metric

2008-05-30

arxiv.org/abs/0805.4828v1

Class.Quant.Grav.25:225022,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages

Scientific paper

10.1088/0264-9381/25/22/225022

We study the eigenvalues of the angular equation arising after the separation of the Dirac equation in the extreme Kerr metric. To this purpose a self-adjoint holomorphic operator family associated to this eigenvalue problem is considered. We show that the eigenvalues satisfy a first order nonlinear differential equation with respect to the black hole mass and we solve it. Finally, we prove that there exist no bound states for the Dirac equation in the aforementioned metric.

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