Finsler geodesics in the presence of a convex function and their applications

TL;DR

This paper investigates the finiteness of geodesics in Finsler manifolds with convex functions and applies the results to Randers and Zermelo metrics, also exploring implications in stationary spacetimes.

Contribution

It establishes conditions for the finite number of geodesics between points in Finsler manifolds with convex functions and extends these results to specific metric types and spacetime models.

Findings

Finite number of geodesics between non-conjugate points in Finsler manifolds with convex functions

Application of results to Randers and Zermelo metrics

Finiteness of lightlike and timelike geodesics in stationary spacetimes

Abstract

We obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.