On a Fermat principle in general relativity. A Morse theory for light rays
type: Item
instance of: scholarly article
title: On a Fermat principle in general relativity. A Morse theory for light rays
zbMATH Open document ID: 0855.53039
DOI: 10.1007/BF02104754
author: Fabio Giannoni
author: Antonio Masiello
published in: General Relativity and Gravitation
publication date: 1996-09-03T00:00:00Z
review text: Among all lightlike curves joining a point \(p\) to a timelike curve \(\gamma\) in a Lorentzian manifold, the geodesics are characterized by stationary arrival time. Here, ``arrival time'' refers to the parametrization of \(\gamma\), and ``stationary'' refers to a minimum, a maximum or a saddle-point. This variational principle can be viewed as a general relativistic version of Fermat's principle. In the paper under review, the authors use this variational principle to develop a Morse theory for lightlike geodesics, similar to the classical Morse theory for Riemannian geodesics in its infinite-dimensional version à la Palais and Smale. To that end the Lorentzian manifold has to satisfy several assumptions that imply, in particular, global hyperbolicity. The authors briefly indicate that their results might have applications to the gravitational lens effect.
reviewed by: Volker Perlick
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 83C10
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 83C50
zbMATH DE Number: 923666
zbMATH Keywords: Fermat's principle
zbMATH Keywords: Morse theory for lightlike geodesics
zbMATH Keywords: global hyperbolicity
zbMATH Keywords: gravitational lens effect
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 923666