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Maximizing curves for the charged-particle action in globally hyperbolic spacetimes

E. Minguzzi
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Abstract

In a globally hyperbolic spacetime any pair of chronologically related events admits a connecting geodesic. We present two theorems which prove that, more generally, under weak assumptions, given a charge-to-mass ratio there is always a connecting solution of the Lorentz force equation having that ratio. A geometrical interpretation of the charged-particle action is given which shows that the constructed solutions are maximizing.

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E. Minguzzi. 2004-12-15. Maximizing curves for the charged-particle action in globally hyperbolic spacetimes. https://arxiv.org/abs/gr-qc/0412074

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