A Fermat principle on Lorentzian manifolds and applications
The authors present a variational principle for lightlike geodesics joining a point to a timelike curve in a Lorentzian manifold. For the techniques used it is essential that the Lorentzian manifold is assumed to admit a global time function, i.e., to be stably causal. If a certain precompactness condition is satisfied, standard results of Lyusternik-Schnirelman theory imply existence and multiplicity results for such lightlike geodesics. Proofs of the statements are only sketched and a more detailed paper is announced to appear elswhere.
scientific article; zbMATH DE number 915083