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Keywords = Chandrasekhar-Page equation

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13 pages, 308 KiB  
Article
On the Eigenvalues of the Fermionic Angular Eigenfunctions in the Kerr Metric
by Davide Batic, Suzan Hamad Abdul Karim and Marek Nowakowski
Entropy 2022, 24(8), 1083; https://doi.org/10.3390/e24081083 - 5 Aug 2022
Viewed by 1606
Abstract
In view of a result recently published in the context of the deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated with the angular equation arising after the separation of the Dirac equation in the Kerr metric, and we show [...] Read more.
In view of a result recently published in the context of the deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated with the angular equation arising after the separation of the Dirac equation in the Kerr metric, and we show how a quasilinear first order PDE for the angular eigenvalues can be derived efficiently. We also prove that it is not possible to obtain an ordinary differential equation for the eigenvalues when the role of the independent variable is played by the particle energy or the black hole mass. Finally, we construct new perturbative expansions for the eigenvalues in the Kerr case and obtain an asymptotic formula for the eigenvalues in the case of a Kerr naked singularity. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
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