Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic space–times

Abstract

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∈ 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.