Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic spacetimes
General Relativity and Quantum Cosmology
2007-05-23 v2
Abstract
We extend the classical Avez-Seifert theorem to trajectories of charged test particles with fixed charge-to-mass ratio. In particular, given two events x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, we find an interval I=]-R,R[ such that for any q/m in I there is a timelike connecting solution of the Lorentz force equation. Moreover, under the assumption that there is no null geodesic connecting x_0 and x_1, we prove that to any value of |q/m| there correspond at least two connecting timelike solutions which coincide only if they are geodesics.
Keywords
Cite
@article{arxiv.gr-qc/0211100,
title = {Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic spacetimes},
author = {E. Caponio and E. Minguzzi},
journal= {arXiv preprint arXiv:gr-qc/0211100},
year = {2007}
}
Comments
AMS-Latex, 9 pages