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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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1432-0916

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Connecting Solutions of the Lorentz Force Equation

Authors: E Minguzzi M Sánchez
Publish Date: 2006/03/11
Volume: 264, Issue: 2, Pages: 349-370
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Abstract

Recent results on the maximization of the chargedparticle action Open image in new window in a globally hyperbolic spacetime are discussed and generalized We focus on the maximization of Open image in new window over a given causal homotopy class Open image in new window of curves connecting two causally related events x 0≤x 1 Action Open image in new window is proved to admit a maximum on Open image in new window and also one in the adherence of each timelike homotopy class C Moreover the maximum σ 0 on Open image in new window is timelike if Open image in new window contains a timelike curve and the degree of differentiability of all the elements is at least C 2In particular this last result yields a complete AvezSeifert type solution to the problem of connectedness through trajectories of charged particles in a globally hyperbolic spacetime endowed with an exact electromagnetic field fixed any chargetomass ratio q/m any two chronologically related events x 0≪x 1 can be connected by means of a timelike solution of the Lorentz force equation corresponding to q/m The accuracy of the approach is stressed by many examples including an explicit counterexample valid for all q/m≠0 in the nonexact case

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