Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric

DOI10.1016/j.anihpc.2010.01.001zbMath1196.58005arXiv0903.3519OpenAlexW1996895845MaRDI QIDQ975293

Antonio Masiello, Erasmo Caponio, Miguel Ángel Javaloyes

Publication date: 9 June 2010

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3519

zbMATH Keywords

Morse theoryconjugate pointsFinsler metricstationary Lorentzian manifolds

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (10)

ON PROJECTIVE EQUIVALENCE AND POINTWISE PROJECTIVE RELATION OF RANDERS METRICS ⋮ Finsler metrics and relativistic spacetimes ⋮ An account on links between Finsler and Lorentz geometries for Riemannian geometers ⋮ On the interplay between Lorentzian causality and Finsler metrics of Randers type ⋮ Addendum to ``Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric ⋮ Riemannian manifolds dual to static spacetimes ⋮ Methods of infinite dimensional Morse theory for geodesics on Finsler manifolds ⋮ Almost isometries of non-reversible metrics with applications to stationary spacetimes ⋮ Splitting lemmas for the Finsler energy functional on the space ofH¹-curves ⋮ On Finsler spacetimes with a timelike Killing vector field

Cites Work

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• A Morse index for geodesics in static Lorentz manifolds
• High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
• A Morse complex for Lorentzian geodesics
• Critical point theory and Hamiltonian systems
• A Morse theory for geodesics on a Lorentz manifold
• A Fermat principle for stationary space-times and applications to light rays
• A timelike extension of Fermat's principle in general relativity and applications
• A Morse lemma for degenerate critical points with low differentiability
• Splitting theorem, Poincaré--Hopf theorem and jumping nonlinear problems
• Morse theory in Hilbert space
• The Morse index theorem in semi-Riemannian geometry
• Homotopy theory of infinite dimensional manifolds
• Periodic geodesics on compact Riemannian manifolds
• On differentiable functions with isolated critical points
• A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole
• On Fermat's principle in general relativity. I. The general case
• A smooth pseudo-gradient for the Lagrangian action functional
• A gravitational lens produces an odd number of images
• A generalization of Morse lemma and its applications
• Gravitational lenses: odd or even images?
• Multiplane gravitational lensing. I. Morse theory and image counting
• The Conjugate Locus of a Riemannian Manifold
• Methods in Nonlinear Analysis
• Riemannian geometry

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