Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222704 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 24 Pages |
Abstract
We propose a finite dimensional setup for the study of lightlike geodesics starting orthogonally to a spacelike (nâ2)-submanifold and arriving orthogonally to the time-slices of an (nâ1)-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.
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Authors
Roberto Giambò, Fabio Giannoni, Paolo Piccione,