On charged particle orbits in dipole magnetic fields around Schwarzschild black holes
Abstract
We consider the motion of charges around Schwarzschild black holes when a magnetic field is present; analysis is focused on the exact solution of Maxwell equations in Schwarzschild spacetime describing dipolar fields generated by current loops around the black hole. This solution deserves particular attention, since it is suggestive of a relation with toroidal currents in accretion discs; with reference to applications of this same field solution, we point out and discuss an existing physical incoherence in past studies, and give the necessary emendation. Critical comparison with previous results is made. The circular orbit characteristics are examined in detail; two sets of solutions are found, both allowing stable circular orbits close to the event horizon, well beyond the Schwarzschild static limit at r = 6M. The existence of potential traps for highly relativistic particles within this same limit is also worth noting, since these same trapped particles may represent an effective source of synchrotron radiation.