Conformally standard stationary spacetimes and Fermat metrics

TL;DR

This paper reviews how Fermat metrics derived from conformally standard stationary spacetimes encode all causal properties, using Finsler geometry to analyze spacetime structure.

Contribution

It consolidates various results connecting Fermat metrics of Randers type with the causal structure of stationary spacetimes.

Findings

Fermat metrics encode all causal aspects of stationary spacetimes

The review links Finsler geometry with relativistic Fermat principle

Provides a unified framework for analyzing spacetime causality

Abstract

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.