Spinning charged test particles in a Kerr-Newman background

We study the motion of a charged spinning test particle (charged top) in a Kerr-Newman gravitational and electromagnetic background (KN background). We first derive the equations of motion of the top in any given background using a Lagrangian approach. It can be seen that the mass is related to the spin by a Regge trajectory, and for the kind of interactions considered here both the mass and the spin are conserved. We prove the existence of constants of motion related to the background symmetries. We show that equatorial plane orbits exist and find the effective potential and the equations for such orbits. We then obtain the conditions to have 100% binding circular orbits in the horizon of a maximal KN background. These conditions are summarized in a figure. We obtain region [in the ($\frac{J}{\mathrm{Mm}}$, $\frac{a}{m}$) plane] giving rise to 100% binding orbits. Only two points of these regions (obtained for spinless charged and spinning neutral test particles, respectively) were known to give 100% binding. Thus, the simultaneous inclusion of spin and charge gives rise to infinitely more possibilities for 100% binding. The velocity of the top in these orbits is timelike or null. No approximations are used throughout this work.