The Dirac point electron in zero-gravity Kerr--Newman spacetime

Abstract

Dirac's wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr--Newman spacetime is studied in a zero-gravity limit; here, "zero-gravity" means $G\to 0$, where $G$ is Newton's constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint; the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. Some of our results extend to a generalization of the zero-$G$ Kerr--Newman spacetime with different electric-monopole-to-magnetic-dipole-moment ratio.

49 pages, 17 figures; referee's comments implemented; the endnotes in the published version appear as footnotes in this preprint

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Cited by in corpus (7)

• Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations
• The effective method to calculate eigenvalues of Chandrasekhar-Page angular equations
• A novel quantum-mechanical interpretation of the Dirac equation
• Stationary solutions of the second-order equation for fermions in Kerr-Newman space-time
• On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetime
• The Einstein-Infeld-Hoffmann legacy in mathematical relativity II. Quantum laws of motion
• Comment on "Quantum phase transitions of Dirac particles in a magnetized rotating curved background: Interplay of geometry, magnetization, and thermodynamics"