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

References in corpus (6)

• General Very Special Relativity is Finsler Geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• The General Very Special Relativity in Finsler Cosmology
• Modified Newton's gravity in Finsler Space as a possible alternative to dark matter hypothesis
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
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• Affine sphere relativity
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Affine sphere spacetimes which satisfy the relativity principle
• On skewon modification of light cone structure
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Electromagnetic and gravitational interactions from Lagrangian mechanics
• Particle motion and scattering in Finslerian Schwarzschild metric
• On the pseudo-Riemann's quartics in Finsler's geometry