Special coordinate systems in pseudo-Finsler geometry and the equivalence principle

Abstract

Special coordinate systems are constructed in a neighborhood of a point or of a curve. Taylor expansions can then be easily inferred for the metric, the connection, or the Finsler Lagrangian in terms of curvature invariants. These coordinates circumvent the difficulties of the normal and Fermi coordinates in Finsler geometry, which in general are not sufficiently differentiable. They are obtained applying the usual constructions to the pullback of a horizontally torsionless connection. The results so obtained are easily specialized to the Berwald or Chern-Rund connections and have application in the study of the equivalence principle in Finslerian extensions of general relativity.

20 pages

References in corpus (4)

• General Very Special Relativity is Finsler Geometry
• Light cones in Finsler spacetime
• The connections of pseudo-Finsler spaces
• On the generalized Jacobi equation

Cited by in corpus (9)

• Geodesics and the magnitude-redshift relation on cosmologically symmetric Finsler spacetimes
• Berwald spacetimes and very special relativity
• Curved spacetimes with local $\kappa$-Poincaré dispersion relation
• Deformed relativity symmetries and the local structure of spacetime
• Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces
• Geometry of weighted Lorentz-Finsler manifolds II: A splitting theorem
• An anisotropic gravity theory
• On the metrizability of $m$-Kropina spaces with closed null 1-form
• A local quantum Mach principle and the metricity of spacetime