Electromagnetic effects on charged particles in a near-horizon-extreme-Kerr geometry

We investigate the motions of charged particles in the near horizon region of an extreme Kerr black hole with weak electromagnetic fields. There is an enhanced symmetry in the near-horizon-extreme-Kerr geometry. We find that when the electromagnetic field respects this enhanced symmetry, which we refer to as the maximally symmetric electromagnetic field, the equations of motion of charged particles get simplified into a set of decoupled first-order differential equations. We discuss the motions of charged particles in two maximally symmetric electromagnetic fields, one being the force-free field and the other being the vacuum fields. Even though the radial motions are similar to the geodesics in near-horizon -extreme-Kerr geometry, the angular motions could be affected by the electromagnetic field significantly. In particular, for the vacuum solution that is produced by a weakly charged black hole, there exist stable vortical motions if the electromagnetic parameter is above the critical value Bc 1/4 p . These vortical ffiffi3 motions do not cross the equatorial planes, and the charged particles in them radiate nonthermally. We discuss the corresponding astrophysical implications.