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

TL;DR

The paper introduces special coordinate systems in pseudo-Finsler geometry that simplify the analysis of metric and connection expansions, aiding the study of the equivalence principle in Finslerian gravity extensions.

Contribution

It develops new coordinate systems in Finsler geometry that are more differentiable than traditional ones, facilitating curvature analysis and applications to gravitational theories.

Findings

Coordinate systems simplify metric and connection expansions.

Applicable to Berwald and Chern-Rund connections.

Aid in studying the equivalence principle in Finsler gravity.

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.