Gravitational lensing in general relativity via bifurcation theory

In a Lorentzian manifold, conjugate points along a lightlike are endpoints of homotopies of lightlike geodesics, up to first order infinitesimals. When studying phenomena on a very large scale in general relativity, like the gravitational lensing effect, the first order approximation is not a valid approach. In this paper we discuss a multiplicity result for light rays issuing from a light source and reaching an observer placed at a conjugate point of a lightlike geodesic using Krasnosel'skii–Rabinowitz bifurcation theory.