On the energy functional on Finsler manifolds and applications to stationary spacetimes

DOI10.1007/s00208-010-0602-7zbMath1228.53052arXivmath/0702323OpenAlexW2064891315MaRDI QIDQ641849

Antonio Masiello, Erasmo Caponio, Miguel Ángel Javaloyes

Publication date: 25 October 2011

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702323

zbMATH Keywords

energy functionalFinsler manifoldstationary spacetime

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 (38)

Closed geodesics on reversible Finsler 2-spheres ⋮ Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness ⋮ Application of the Gauss-Bonnet theorem to lensing in the NUT metric ⋮ ON PROJECTIVE EQUIVALENCE AND POINTWISE PROJECTIVE RELATION OF RANDERS METRICS ⋮ A note on the existence of tubular neighbourhoods on Finsler manifolds and minimization of orthogonal geodesics to a submanifold ⋮ Finsler metrics and relativistic spacetimes ⋮ Stationary-complete spacetimes with non-standard splittings and pre-Randers metrics ⋮ Multiple connecting geodesics of a Randers-Kropina metric via homotopy theory for solutions of an affine control system ⋮ A Finsler geodesic spray paradigm for wildfire spread modelling ⋮ On Finsler transnormal functions ⋮ An account on links between Finsler and Lorentz geometries for Riemannian geometers ⋮ Snell’s law revisited and generalized via Finsler geometry ⋮ Gravitational lensing effect in the universe with a Finsler background ⋮ Wind Riemannian spaceforms and Randers-Kropina metrics of constant flag curvature ⋮ Convex domains of Finsler and Riemannian manifolds ⋮ The Morse index theorem in the case of two variable endpoints in conic Finsler manifolds ⋮ 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 ⋮ On singular Finsler foliation ⋮ A multiplicity result for orthogonal geodesic chords in Finsler disks ⋮ Connecting and closed geodesics of a Kropina metric ⋮ Closed geodesics in Lorentzian surfaces ⋮ Noncommutative black hole in the Finslerian spacetime ⋮ On the growth rate of geodesic chords ⋮ On the splitting problem for Lorentzian manifolds with an \({\mathbb {R}}\)-action with causal orbits ⋮ Almost isometries of non-reversible metrics with applications to stationary spacetimes ⋮ Functional regularity properties for light rays in general relativity ⋮ Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect ⋮ Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds ⋮ A note on the Sagnac effect in general relativity as a Finslerian effect ⋮ Splitting lemmas for the Finsler energy functional on the space ofH¹-curves ⋮ Growth conditions, Riemannian completeness and Lorentzian causality ⋮ On Finsler spacetimes with a timelike Killing vector field ⋮ A COUNTEREXAMPLE TO GUILLEMIN'S ZOLLFREI CONJECTURE ⋮ Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold ⋮ Boundary rigidity for Randers metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geodesics in stationary spacetimes and classical Lagrangian systems
• High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
• Finsler spinoptics
• Finsler geometry, relativity and gauge theories
• The theory of sprays and Finsler spaces with applications in physics and biology
• A Fermat principle for stationary space-times and applications to light rays
• A timelike extension of Fermat's principle in general relativity and applications
• Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesics
• A sphere theorem for non-reversible Finsler metrics
• A note on the boundary of a static Lorentzian manifold.
• Zermelo navigation on Riemannian manifolds
• Gravitational lensing from a spacetime perspective
• A general-relativistic Fermat principle for extended light sources and extended receivers
• Critical point theorems on Finsler manifolds
• Fermat principle in Finsler spacetimes
• Lusternik-Schnirelman theory on Banach manifolds
• Morse theory on Hilbert manifolds
• The Avez–Seifert theorem for the relativistic Lorentz force equation
• On Fermat's principle in general relativity. I. The general case
• Morse Theory. (AM-51)
• Category of loop spaces of open subsets in euclidean space
• CONVEX REGIONS IN THE GEOMETRY OF PATHS
• The Conjugate Locus of a Riemannian Manifold
• The Large Scale Structure of Space-Time
• On the existence of light-like geodesics on conformally stationary Lorentzian manifolds
• Riemannian geometry

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