• DOI:10.1142/9789811269776_0049
• Corpus ID: 241033049

The point spectrum of the Dirac Hamiltonian on the zero-gravity Kerr-Newman spacetime

@article{Kiessling2021ThePS,
  title={The point spectrum of the Dirac Hamiltonian on the zero-gravity Kerr-Newman spacetime},
  author={Michael K.-H. Kiessling and Eric Ling and A. Shadi Tahvildar-Zadeh},
  journal={The Sixteenth Marcel Grossmann Meeting},
  year={2021}
}

• M. Kiessling, E. Ling, A. Tahvildar-Zadeh
• Published 3 November 2021
• Physics, Mathematics
• The Sixteenth Marcel Grossmann Meeting

The zero-gravity Kerr-Newman (zGKN) spacetime has been studied extensively. In reference 9 it was shown that the discrete spectrum of the Dirac Hamiltonian on zGKN is nonempty. In an upcoming paper we classify the discrete spectrum and show that the spectrum is indexed by three integers. See Theorem 2.1 below. It was conjectured that the discrete spectrum of the Dirac Hamiltonian on zGKN should converge to the Bohr-Sommerfeld spectrum of the usual Hydrogen problem on Minkowski spacetime with a Coulomb potential in the limit as the ring radius of zGKN approaches 0. This problem remains open but a first step in solving this problem is to determine which states in the zGKN spectrum should correspond to which states in the usual hydrogenic spectrum. For example, which states should correspond to 1s1/2, 2s1/2, 2p1/2, etc.? The purpose of this paper is to provide this correspondence.