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

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

2004-12-15

arxiv.org/abs/gr-qc/0412074v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 6 figures, contribution to the proceedings of the "9th International conference on differential geometry and its app

Scientific paper

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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