Two-point boundary value problems in relativistic dynamics (Q1358495)

The paper starts with an action functional for the motion of a test particle in a Lorentzian manifold \((M,g)\), composed of a velocity term, a Maxwell field term, and a Newton potential term. An extremal curve is taken as the projection of a geodesic in a Kaluza-Klein manifold, which is a bundle over \(M\) and is equipped with a bundle metric composed of \(g\), a Maxwell potential, and the Newton potential. It is shown that there exists an extremal with prescribed boundary points if \((M,g)\) is globally hyperbolic and some other mild conditions are satisfied. The proof uses arguments of variational calculus, homotopy, cohomology, and the theory of causal structures.