Conformally standard stationary spacetimes and Fermat metrics
  In this review, we collect several results for conformally standard stationary spacetimes (SxR,g) obtained in terms of a Finsler metric of Randers type on the orbit manifold S that we call Fermat metric. This metric is obtained by applying the relativistic Fermat principle and it turns out that it encodes all the causal aspects of the spacetime. 
Miguel Angel Javaloyes
math.DG gr-qc