On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetime

TL;DR

This paper analyzes the discrete Dirac spectrum of a point electron in a zero-gravity Kerr-Newman spacetime, revealing a triplet of integers related to dynamical system orbits and connecting it to the hydrogenic spectrum.

Contribution

It characterizes the Dirac spectrum in the zero-G Kerr-Newman spacetime and relates it to known hydrogenic spectra, providing a novel mathematical framework.

Findings

Spectrum characterized by a triplet of integers

Established a dictionary linking the spectrum to hydrogenic Dirac spectrum

Presented numerical illustrations and listed open problems

Abstract

The discrete spectrum of the Dirac operator for a point electron in the maximal analytically extended Kerr--Newman spacetime is determined in the zero-$G$ limit (z$G$KN), under some restrictions on the electrical coupling constant and on the radius of the ring-singularity of the z$G$KN spacetime. The spectrum is characterized by a triplet of integers, associated with winding numbers of orbits of dynamical systems on cylinders. A dictionary is established that relates the spectrum with the known hydrogenic Dirac spectrum. Numerical illustrations are presented. Open problems are listed.