Generalized Wilkins effect and selected orbits in a Kerr-Newman geometry

Wilkins has pointed out that, in addition to the periodicities associated with circular orbits in the equatorial plane of a Kerr geometry, there exist periodicities connected with the longitudinal motion of particles. We extend this result to spherical orbits of charged particles in a Kerr-Newman geometry. We give explicit examples of nonspherical orbits, illustrating dragging of inertial frames and these longitudinal periodicities. The relevance of these results for the physics of collapsed objects is discussed.