  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.
