Light cones in Finsler spacetime

Abstract

Some foundational results on the geometry of Lorentz-Minkowski spaces and Finsler spacetimes are obtained. We prove that the local light cone structure of a reversible Finsler spacetime with more than two dimensions is topologically the same as that of Lorentzian spacetimes: at each point we have just two strictly convex causal cones which intersect only at the origin. Moreover, we prove a reverse Cauchy-Schwarz inequality for these spaces and a corresponding reverse triangle inequality. The Legendre map is proved to be a diffeomorphism in the general pseudo-Finsler case provided the dimension is larger than two.

24 pages. v2: modified Example 1 v3: updated references, matches published version

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Cited by in corpus (39)

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• Finsler geometry as a model for relativistic gravity
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Mathematical foundations for field theories on Finsler spacetimes
• Standard static Finsler spacetimes
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• Schwarzschild-like solutions in Finsler-Randers gravity
• Weak field equations and generalized FRW cosmology on the tangent Lorentz bundle
• On Finsler spacetimes with a timelike Killing vector field
• Redshift in Finsler spacetimes
• On the analyticity of static solutions of a field equation in Finsler gravity
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Applications of the Schwarzschild-Finsler-Randers model
• Affine sphere relativity
• Geometry of weighted Lorentz-Finsler manifolds I: Singularity theorems
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Affine sphere spacetimes which satisfy the relativity principle
• On skewon modification of light cone structure
• Special coordinate systems in pseudo-Finsler geometry and the equivalence principle
• Volume forms for time orientable Finsler spacetimes
• Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem
• Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• A variational setting for an indefinite Lagrangian with an affine Noether charge
• Metrizability of SO(3)-invariant connections: Riemann versus Finsler
• Comparison theorems on weighted Finsler manifolds and spacetimes with $\epsilon$-range
• A divergence theorem for pseudo-Finsler spaces
• Electromagnetic and gravitational interactions from Lagrangian mechanics
• Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge
• The conformal transformation of the night sky
• Timelike Hilbert and Funk geometries
• Kinetic gases in static spherically symmetric modified dispersion relations
• On the pseudo-Riemann's quartics in Finsler's geometry
• Particle motion and scattering in Finslerian Schwarzschild metric