Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic spacetimes

We extend the classical Avez-Seifert theorem to trajectories of charged test particles with fixed charge-to-mass ratio. In particular, given two events x(0) and x(1), with x(1) in the chronological future of x(0), we find an interval I =] - R, R[ such that for any q/m epsilon I there is a timelike connecting solution of the Lorentz force equation. Moreover, under the assumption that there is no null geodesic connecting x(0) and x(1), we prove that to any value of \q/m\ there correspond at least two connecting timelike solutions which coincide only if they are geodesics.