Motion of charged particles around a magnetized/electrified black hole

Geodesic equations of timelike and null charged particles in the Ernst metric are studied. We consider two distinct forms of the Ernst solution where the Maxwell potential represents either a uniform electric or magnetic field. Circular orbits in various configurations are considered, as well as their perturbations and stability. We find that the electric field strength must be below a certain charge-dependent critical value for these orbits to be stable. The case of the magnetic Ernst metric contains a limit which reduces to the Melvin magnetic universe. In this case the equations of motion are solved to reveal cycloidlike or trochoidlike motion, similar to those found by Frolov and Shoom around black holes immersed in test magnetic fields.