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Off-equatorial circular orbits with constant latitudes (halo orbits) ofelectrically charged particles exist near compact objects. In the previouspaper, we discussed this kind of motion and demonstrated the existence ofminima of the two-dimensional effective potential which correspond to thestable halo orbits. Here, we relax previous assumptions of the pseudo-Newtonianapproach for the gravitational field of the central body and study propertiesof the halo orbits in detail. Within the general relativistic approach, wecarry out our calculations in two cases. Firstly, we examine the case of arotating magnetic compact star. Assuming that the magnetic field axis and therotation axis are aligned with each other, we study the orientation of motionalong the stable halo orbits. In the poloidal plane, we also discuss shapes ofthe related effective potential halo lobes where the general off-equatorialmotion can be bound. Then we focus on the halo orbits near a Kerr black holeimmersed in an asymptotically uniform magnetic field of external origin. Wedemonstrate that, in both the cases considered, the lobes exhibit two differentregimes, namely, one where completely disjoint lobes occur symmetrically aboveand below the equatorial plane, and another where the lobes are joined acrossthe plane. A possible application of the model concerns the structure ofputative circumpulsar discs consisting of dust particles. We suggest that theparticles can acquire a small (but non-zero) net electric charge, and thisdrives them to form the halo lobes.

classical and quantum gravity

Off-equatorial orbits in strong gravitational fields near compact  objects -- II: halo motion around magnetic compact stars and magnetized black  holes