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On the discrete Dirac spectrum of a point electron in the zero-gravity Kerr-Newman spacetime (2112.00073v1)
Published 30 Nov 2021 in math-ph, gr-qc, math.AP, math.DS, math.MP, and quant-ph
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.