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arXiv · 1012.4467

The causal structure of spacetime is a parameterized Randers geometry

Jozef Skakala·Matt Visser
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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.

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Jozef Skakala, Matt Visser. 2010-12-20. The causal structure of spacetime is a parameterized Randers geometry. https://doi.org/10.1088/0264-9381%2F28%2F6%2F065007

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