On the definition and examples of cones and Finsler spacetimes

DOI10.1007/s13398-019-00736-yzbMath1432.53091arXiv1805.06978OpenAlexW2803948559MaRDI QIDQ2289387

Miguel Ángel Javaloyes, Miguel Sánchez

Publication date: 28 January 2020

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.06978

zbMATH Keywords

cone structureZermelo navigation problemFinsler spacetimegeneralized Fermat principleLorentz-Finsler metrics and normsstatic and stationary spacetimes

Mathematics Subject Classification ID

Relativistic gravitational theories other than Einstein's, including asymmetric field theories (83D05) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Kinematics of a particle (70B05)

Related Items (29)

Ricci-flat Finsler metrics by warped product ⋮ Comparison theorems on weighted Finsler manifolds and spacetimes with \(\epsilon\)-range ⋮ Electromagnetic and gravitational interactions from Lagrangian mechanics ⋮ Mathematical foundations for field theories on Finsler spacetimes ⋮ On the metrizability of m-Kropina spaces with closed null one-form ⋮ The flag curvature of a submanifold of a Randers-Minkowski space in terms of Zermelo data ⋮ Deforming convex bodies in Minkowski geometry ⋮ Causal hierarchy in modified gravity ⋮ Identifying Berwald Finsler geometries ⋮ Finsler gravitational waves of (α, β)-type and their observational signature ⋮ A variational setting for an indefinite Lagrangian with an affine Noether charge ⋮ Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds ⋮ An account on links between Finsler and Lorentz geometries for Riemannian geometers ⋮ Snell’s law revisited and generalized via Finsler geometry ⋮ Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces ⋮ A General Model for Wildfire Propagation with Wind and Slope ⋮ Finsler pp-waves and the Penrose limit ⋮ Kinetic gases in static spherically symmetric modified dispersion relations ⋮ The Morse index theorem in the case of two variable endpoints in conic Finsler manifolds ⋮ On the regularity of Cauchy hypersurfaces and temporal functions in closed cone structures ⋮ Gravitational quantum dynamics: a geometrical perspective ⋮ Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds ⋮ Time-extremal navigation in arbitrary winds on conformally flat Riemannian manifolds ⋮ Applications of cone structures to the anisotropic rheonomic Huygens' principle ⋮ The Cayley cubic and differential equations ⋮ Inequalities from Lorentz-Finsler norms ⋮ Globally hyperbolic spacetimes: slicings, boundaries and counterexamples ⋮ Lightlike hypersurfaces and time-minimizing geodesics in cone structures ⋮ Anisotropic connections and parallel transport in Finsler spacetimes

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