Structure of external electromagnetic field around a slowly rotating compact object and charged-particle trajectories therein

In this paper they have discussed the trajectories of a charged particle in a dipole magnetic field and quadrupole electric field superposed on the external space-time of a very slowly rotating mass represented by a first-order correction to the Schwarzschild geometry. The metric, which is an approximate form of the Hartle-Thorne metric, includes corrections of linear order in (ω = 2J / r3) only. Trapped bound orbits exist both for co-and contra-rotating particles as evidenced from the structure of the potential wells for various combinations of the physical parameters