On the existence of maximizing curves for the charged-particle action

Details On the existence of maximizing curves for the charged-particle action On the existence of maximizing curves for the charged-particle action

2003-03-28

arxiv.org/abs/gr-qc/0303111v2

Class.Quant.Grav. 20 (2003) 4169-4175

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

AMSLatex, 6 pages

Scientific paper

10.1088/0264-9381/20/19/303

The classical Avez-Seifert theorem is generalized to the case of the Lorentz force equation for charged test particles with fixed charge-to-mass ratio. Given two events x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, and a ratio q/m, it is proved that a timelike connecting solution of the Lorentz force equation exists provided there is no null connecting geodesic and the spacetime is globally hyperbolic. As a result, the theorem answers affirmatively to the existence of timelike connecting solutions for the particular case of Minkowski spacetime. Moreover, it is proved that there is at least one C^{1} connecting curve that maximizes the functional I[\gamma]=\int_{\gamma} ds+q/(mc^2) \omega over the set of C^{1} future-directed non-spacelike connecting curves.

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