  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.
