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

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

2008-03-04

arxiv.org/abs/0803.0488v2

Mathematics

Differential Geometry

15 pages. Lemma 2.1 modified due to an incorrect statement

Scientific paper

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.

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