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

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.

15 pages. Lemma 2.1 modified due to an incorrect statement

References in corpus (2)

• Multiple closed geodesics on bumpy Finsler $n$-spheres
• On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes