Lightlike periodic trajectories in space-times (Q678135)

In this paper the author studies existence and multiplicity of lightlike trajectories (light rays with closed spatial component) on a class of conformally stationary Lorentzian manifolds. The spatial component of the manifold is not necessarily a compact manifold. Moreover, the case of manifolds with boundary is considered. The proof is obtained applying Lyusternik-Schnirelmann theory to a functional whose critical points are related to the lightlike trajectories of the manifold. Such a functional is obtained by means of an extension to general relativity of the classical Fermat variational principle of geometrical optics.