Generalised time functions and finiteness of the Lorentzian distance
Differential Geometry
2017-03-10 v3 General Relativity and Quantum Cosmology
Abstract
We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional description of the Lorentzian distance extending the work of Franco and Moretti.
Keywords
Cite
@article{arxiv.1412.5652,
title = {Generalised time functions and finiteness of the Lorentzian distance},
author = {Adam Rennie and Ben E. Whale},
journal= {arXiv preprint arXiv:1412.5652},
year = {2017}
}
Comments
22 pages. Some imprecisions clarified compared to first version