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 (LorentzFinsler) 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 for globally hyperbolic Lorentzian spacetimes.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 February 2018
 DOI:
 10.1088/17426596/968/1/012009
 arXiv:
 arXiv:1711.00076
 Bibcode:
 2018JPhCS.968a2009M
 Keywords:

 Mathematics  Differential Geometry;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 11 pages. v2: minor changes, matches version accepted for publication in the Proceedings of the meeting "NonRegular Spacetime geometry", 2022 June 2017, Firenze