On Finsler spacetimes with a timelike Killing vector field

Abstract

We study Finsler spacetimes and Killing vector fields taking care of the fact that the generalized metric tensor associated to the Lorentz-Finsler function $L$ is in general well defined only on a subset of the slit tangent bundle. We then introduce a new class of Finsler spacetimes endowed with a timelike Killing vector field that we call stationary splitting Finsler spacetimes. We characterize when a Finsler spacetime with a timelike Killing vector field is locally a stationary splitting. Finally, we show that the causal structure of a stationary splitting is the same of one of two Finslerian static spacetimes naturally associated to the stationary splitting.

28 pages, AMSLaTex. v3: First part of the introduction and conclusions section expanded, some new references added; v3 matches the published version

References in corpus (8)

• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Light cones in Finsler spacetime
• Finsler-Randers Cosmology: dynamical analysis and growth of matter perturbations
• Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles

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• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
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• A variational setting for an indefinite Lagrangian with an affine Noether charge
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