Abstract
In this paper we prove an extension of the Avez–Seifert theorem to the relativistic Lorentz force equation. Let (M,g) be a globally hyperbolic space–time, F an exact 2-form on M representing the electromagnetic field, F̂ the Lorentz force associated to F, and q a charge for a test particle. Let p0 and p1 be two chronologically related points on M, then there exists a future-pointing timelike solution of the Lorentz force equation Dsż=qF̂(z)[ż], connecting p0 and p1.
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