Maximizing curves for the charged-particle action in globally hyperbolic spacetimes
arXiv:gr-qc/0412074
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.
16 pages, 6 figures, contribution to the proceedings of the "9th International conference on differential geometry and its applications" Prague, August 30 - September 3, 2004