The representation of spacetime through steep time functions

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.

11 pages. v2: minor changes, matches version accepted for publication in the Proceedings of the meeting "Non-Regular Spacetime geometry", 20-22 June 2017, Firenze