Light cones in Finsler spacetime

Understand

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.