Anisotropic conformal invariance of lightlike geodesics in pseudo-Finsler manifolds

TL;DR

This paper demonstrates that lightlike geodesics and their focal points in pseudo-Finsler manifolds remain invariant under anisotropic conformal transformations, with implications for Finsler spacetime analysis.

Contribution

It establishes the invariance of lightlike geodesics and focal points under anisotropic conformal changes using the Chern connection and anisotropic calculus.

Findings

Lightlike geodesics are preserved up to reparametrization.

Focal points are invariant under anisotropic conformal transformations.

Results have applications in the study of Finsler spacetimes.

Abstract

In this paper, we prove that lightlike geodesics of a pseudo-Finsler manifold and its focal points are preserved up to reparametrization by anisotropic conformal changes, using the Chern connection and the anisotropic calculus and the fact that geodesics are critical points of the energy functional and Jacobi fields, the kernel of its index form. This result has applications to the study of Finsler spacetimes.