A finite dimensional approach to light rays in General Relativity. (March 2018)

• Record Type: Journal Article
• Authors: Giambò, Roberto; Giannoni, Fabio; Piccione, Paolo
• Is Part Of: Nonlinear analysis. Volume 168(2018)
• Page Start: 198
• Page End: 221
• Publication Date: 2018-03
• Subjects: Relativistic Fermat principle -- Morse index; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.11.014
• Languages: English
• ISSNs: 0362-546X

Abstract

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.