Fermats principle, Morse theory and applications to the gravitational lens effect

DOI10.1016/S0362-546X(97)00036-9zbMath0889.53063MaRDI QIDQ4378422

Volker Perlick

Publication date: 29 May 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacesMorse theorygeodesicsgeneral relativityLorentzian geometryFermat's principlegravitational lens effect

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational principles in infinite-dimensional spaces (58E30) Applications of differential geometry to physics (53Z05) General relativity (83C99) Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (1)

A timelike extension of fermat's principle in general relativity. Comparisons with the lightlike case

Cites Work

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• A Morse theory for geodesics on a Lorentz manifold
• A general approach to Morse theory
• Morse theory and a non-linear generalization of the Dirichlet problem
• Morse theory on Hilbert manifolds
• On Fermat's principle in general relativity. I. The general case
• A gravitational lens produces an odd number of images
• Infinite dimensional Morse theory and Fermat’s principle in general relativity. I
• A generalized Morse theory
• Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field

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