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

E. Caponio·E. Minguzzi
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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 in 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.

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E. Caponio, E. Minguzzi. 2003-02-12. Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic spacetimes. https://doi.org/10.1016/s0393-0440(03)00073-1

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