The causal structure of spacetime is a parameterized Randers geometry

TL;DR

This paper demonstrates that the causal structure of general non-stationary spacetimes can be fully described by a parameterized, time-dependent Randers geometry, extending previous stationary spacetime results.

Contribution

It extends the isomorphism between stationary spacetimes and Randers geometries to non-stationary cases using ADM decomposition.

Findings

Causal structure encoded in time-dependent Randers spaces

Reconstruction of null cones from Randers geometry

Extension of Fermat principle to non-stationary spacetimes

Abstract

There is a by now well-established isomorphism between stationary 4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries - these Randers geometries being a particular case of the more general class of 3-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes - the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (time-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.