The representation of spacetime through steep time functions
Differential Geometry
2018-02-26 v2 General Relativity and Quantum Cosmology
Mathematical Physics
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.
Cite
@article{arxiv.1711.00076,
title = {The representation of spacetime through steep time functions},
author = {E. Minguzzi},
journal= {arXiv preprint arXiv:1711.00076},
year = {2018}
}
Comments
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