Shortening null geodesics in Lorentzian manifolds. Applications to closed light rays (Q1385071)

The authors show the existence of one spatially closed geodesic on a regular, conformally stationary Lorentzian manifold \({\mathcal M}\) having a non-contractible, light-convex, timelike cylinder. The result is obtained by using an extension of the classical Fermat principle in optics and a shortening argument for light rays, similar to the shortening method for geodesics in Riemannian manifolds. The paper closes with an appendix containing some results on the existence and regularity of minimum points for action integrals whose Lagrangian satisfies a quasi-Finsler condition.