Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness

DOI10.1007/s12220-015-9572-zzbMath1348.53069arXiv1112.3892OpenAlexW2053839160MaRDI QIDQ282784

Erasmo Caponio, Anna Valeria Germinario, Miguel Sánchez

Publication date: 12 May 2016

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3892

zbMATH Keywords

gravitational lensingFinsler manifoldRanders metricasymptotic flatnessconvex boundarystationary spacetimetime-like and light-like geodesics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items

An account on links between Finsler and Lorentz geometries for Riemannian geometers ⋮ Riemannian manifolds dual to static spacetimes ⋮ Light bending in a two black hole metric ⋮ Structure of globally hyperbolic spacetimes-with-timelike-boundary ⋮ Almost isometries of non-reversible metrics with applications to stationary spacetimes ⋮ Standard static Finsler spacetimes ⋮ On Finsler spacetimes with a timelike Killing vector field ⋮ Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold

Cites Work

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• On the final definition of the causal boundary and its relation with the conformal boundary
• Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic space-times
• Convex domains of Finsler and Riemannian manifolds
• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• On the interplay between Lorentzian causality and Finsler metrics of Randers type
• Convex defining functions for convex domains
• Connecting solutions of the Lorentz force equation do exist
• On the Riemannian Penrose inequality in dimensions less than eight
• On the existence of geodesics on stationary Lorentz manifolds with convex boundary
• A Fermat principle for stationary space-times and applications to light rays
• Shortening null geodesics in Lorentzian manifolds. Applications to closed light rays
• Elliptic partial differential equations of second order
• Convexity of domains of Riemannian manifolds
• A note on the boundary of a static Lorentzian manifold.
• Gravitational lensing from a spacetime perspective
• Remarks on some variational problems on non-complete manifolds.
• Geodesic connectedness of semi-Riemannian manifolds.
• Stationary black holes: uniqueness and beyond
• Global hyperbolicity and Palais-Smale condition for action functionals in stationary spacetimes
• Geodesic connectedness of multiwarped spacetimes
• Initial data for stationary spacetimes near spacelike infinity
• Infinitesimal and Local Convexity of a Hypersurface in a Semi-Riemannian Manifold
• Globally hyperbolic spacetimes can be defined as ‘causal’ instead of ‘strongly causal’
• 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 note on the existence of standard splittings for conformally stationary spacetimes
• Finsler geodesics in the presence of a convex function and their applications
• CONVEXITY CONDITIONS ON THE BOUNDARY OF A STATIONARY SPACETIME AND APPLICATIONS
• The mass of an asymptotically flat manifold
• Category of loop spaces of open subsets in euclidean space
• Timelike periodic trajectories in spatially compact Lorentz manifolds
• Exact Solutions of Einstein's Field Equations
• A topological method for geodesic connectedness of space–times: Outer Kerr space–time
• Gromov, Cauchy and causal boundaries for Riemannian, Finslerian and Lorentzian manifolds
• Killing vectors in asymptotically flat space–times. I. Asymptotically translational Killing vectors and the rigid positive energy theorem
• On the causal properties of warped product spacetimes
• The Large Scale Structure of Space-Time
• General Relativity
• Conformal infinity