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

摘要

We extend the classical Avez-Seifert theorem to trajectories of charged testparticles with fixed charge-to-mass ratio. In particular, given two eventsx_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, we find aninterval I=]-R,R[ such that for any q/m in I there is a timelike connectingsolution of the Lorentz force equation. Moreover, under the assumption thatthere 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 whichcoincide only if they are geodesics.