A finite dimensional approach to light rays in General Relativity. (March 2018) - Giambò, Roberto; Giannoni, Fabio; Piccione, Paolo
Abstract: We propose a finite dimensional setup for the study of lightlike geodesics starting orthogonally to a spacelike ( n − 2 ) -submanifold and arriving orthogonally to the time-slices of an ( n − 1 ) -dimensional timelike submanifold of a n -dimensional spacetime. Under a transversality and a nonfocality assumption, we prove a finite dimensional reduction of a general relativistic Fermat principle, and we give a formula for the Morse index. We present some applications to bifurcation theory, and we conclude the paper with the discussion of some examples that illustrate our results.