Abstract
Recent results on the maximization of the charged-particle 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 x0≤x1. 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 σ0 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 C2).
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