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

Abstract

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.

arXiv comment13 pages

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• On Born approximation in black hole scattering
• Analytical treatment of SUSY Quasi-normal modes in a non-rotating Schwarzschild black hole
• On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric