**Publication date:** Jul 2010

**Abstract:**

Off-equatorial circular orbits with constant latitudes (halo orbits) of

electrically charged particles exist near compact objects. In the

previous paper, we discussed this kind of motion and demonstrated the

existence of minima of the two-dimensional effective potential which

correspond to the stable halo orbits. Here, we relax previous

assumptions of the pseudo-Newtonian approach for the gravitational field

of the central body and study properties of the halo orbits in detail.

Within the general relativistic approach, we carry out our calculations

in two cases. Firstly, we examine the case of a rotating magnetic

compact star. Assuming that the magnetic field axis and the rotation

axis are aligned with each other, we study the orientation of motion

along the stable halo orbits. In the poloidal plane, we also discuss

shapes of the related effective potential halo lobes where the general

off-equatorial motion can be bound. Then we focus on the halo orbits

near a Kerr black hole immersed in an asymptotically uniform magnetic

field of external origin. We demonstrate that, in both the cases

considered, the lobes exhibit two different regimes, namely one where

completely disjoint lobes occur symmetrically above and below the

equatorial plane, and another where the lobes are joined across the

plane. A possible application of the model concerns the structure of

putative circumpulsar discs consisting of dust particles. We suggest

that the particles can acquire a small (but non-zero) net electric

charge, and this drives them to form the halo lobes.

**Authors:**

Kovář, J.; Kopáček, O.; Karas, V.; Stuchlík, Z.;