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

TL;DR

This paper investigates the behavior of a Dirac electron in a zero-gravity Kerr--Newman spacetime, establishing self-adjointness of the Hamiltonian and analyzing its spectrum, including conditions for point spectrum presence.

Contribution

It provides a rigorous analysis of the Dirac equation in a zero-gravity Kerr--Newman spacetime, extending previous results to generalized cases with different electromagnetic moments.

Findings

Hamiltonian is essentially self-adjoint

Spectrum is symmetric about zero with a gap

Under certain conditions, a point spectrum exists

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.