Motion of charged particles on the Reissner-NordströM (anti)-de Sitter black hole spacetime

We study the motion of relativistic, electrically charged point particles in the background of charged black holes with nontrivial asymptotic behavior. We compute the exact trajectories of massive particles and express them in terms of elliptic Jacobi functions. As a result, we obtain a detailed description of particles orbits in the gravitational field of Reissner-Nordström (anti)-de Sitter black hole, depending of their charge, mass and energy.