$t$-periodic light rays in conformally stationary spacetimes via Finsler geometry

TL;DR

This paper investigates the existence and multiplicity of $t$-periodic light rays in conformally stationary spacetimes using Finsler geometry, extending classical theorems and providing bounds on periods based on curvature conditions.

Contribution

It extends classical multiplicity theorems to Finsler manifolds and applies these results to analyze $t$-periodic light rays in specific spacetime models.

Findings

Proved multiple existence results for $t$-periodic light rays.

Constructed examples with finitely many $t$-periodic light rays.

Derived lower bounds for light ray periods based on curvature.

Abstract

In this paper we prove several multiplicity results of $t$-periodic light rays in conformally stationary spacetimes using the Fermat metric and the extensions of the classical theorems of Gromoll-Meyer and Bangert-Hingston to Finsler manifolds. Moreover, we exhibit some stationary spacetimes with a finite number of $t$-periodic light rays and compute a lower bound for the period of the light rays when the flag curvature of the Fermat metric is $\eta$-pinched.