Acceleration of charged particles from near-extremal rotating black holes embedded in magnetic fields

The aim of the present article is to evaluate the motion of charged test particles in the vicinity of a near-extremal rotating black hole in the presence of magnetic fields. Euler-Lagrange motion equations and effective potential methods are used to characterize the motion out of the equatorial plane. Such approach is of peculiar significance if it is considered, e.g., accretion processes onto rotating black holes. In general investigations concerning accretion focus mostly on the simplest case of particles moving in the equatorial plane. Here it will be considered that particles initially moving around some particular orbit may be perturbed by a kick along the $θ$ direction, giving rise to other possible orbits. We confirm the possibility that ultra high energy cosmic rays would be produced at the very center of AGNs, for a specific range of magnetic field magnitudes, since it is possible that ultra-high center-of-mass energies can be produced by particles colliding near the horizon of fastly rotating black holes.