Motions and worldline deviations in Einstein-Maxwell theory

We examine the motion of charged particles in gravitational and electromagn etic background fields. We study in particular the deviation of worldlines, describing the relative acceleration between particles on different spacet ime trajectories. Two special cases of background fields are considered in detail: (a) pp-waves, a combination of gravitational and electromagnetic po larized plane waves travelling in the same direction; (b) the Reissner-Nord strom solution. We perform a non-trivial check by computing the precession of the periastron for a charged particle in the Reissner-Nordstrom geometry both directly by solving the geodesic equation, and using the worldline de viation equation. The results agree to the order of approximation considere d.