Light cones in Finsler spacetime. (English) Zbl 1310.83007
Summary: 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.
MSC:
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 53B40 | Local differential geometry of Finsler spaces and generalizations (areal metrics) |
| 83A05 | Special relativity |
| 51M05 | Euclidean geometries (general) and generalizations |
Keywords:
light cones; Finsler spacetime; Lorentz-Minkowski spaces; Cauchy-Schwarz inequality; triangle inequality; Legendre mapReferences:
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