A Fermat Principle on Lorentzian manifolds and applications

AbstractWe present a version of the Fermat Principle to Lorentzian manifolds endowed with a time function. The principle is used to obtain some results concerning the existence and multiplicity of light rays, generalizing part of the work in [1–3]. At this time, the results are announced and discussed, while the details of their proofs are left to a forthcoming paper [4]