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The causal structure of spacetime is a parameterized Randers geometry
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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.
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Wind-Finslerian structure of black holes
The causal structure of black holes, including horizons and interiors, can be encoded in wind-Finsler metrics whose shifted indicatrices track null geodesics.
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