On the Eigenvalues of the Fermionic Angular Eigenfunctions in the Kerr Metric

Davide Batic, Suzan Hamad Abdul Karim, Marek Nowakowski

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageBritish English
Article number1083
JournalEntropy
Volume24
Issue number8
DOIs
StatePublished - Aug 2022

Keywords

  • Chandrasekhar-Page equation
  • Dirac equation
  • Kerr black hole
  • linear hamiltonian systems

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