2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58352In this paper we use a general version of Fermat's principle for light rays in General Relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. As a physical meaning, one can apply the Morse relations to have a mathematical description of the "gravitational lens effect" in a very general context.Plain TeX, 42 pagesMathematical Physicstext