Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic spacetimes
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 x0 and x1, with x1 in the chronological future of x0, we find an interval I=]-R,R[ such that for any q/m in I there is a timelike connecting solution of the Lorentz force equation. Moreover, under the assumption that there is no null geodesic connecting x0 and x1, we prove that to any value of |q/m| there correspond at least two connecting timelike solutions which coincide only if they are geodesics.
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