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The representation of spacetime through steep time functions (1711.00076v2)
Published 31 Oct 2017 in math.DG, gr-qc, math-ph, and math.MP
Abstract: In a recent work I showed that the family of smooth steep time functions can be used to recover the order, the topology and the (Lorentz-Finsler) distance of spacetime. In this work I present the main ideas entering the proof of the (smooth) distance formula, particularly the product trick which converts metric statements into causal ones. The paper ends with a second proof of the distance formula valid in globally hyperbolic Lorentzian spacetimes.
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