On differentiability of volume time functions
General Relativity and Quantum Cosmology
2016-12-02 v2 Mathematical Physics
math.MP
Abstract
We show differentiability of a class of Geroch's volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally anti-Lipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably causal spacetimes Hawking's time function can be uniformly approximated by smooth time functions with timelike gradient.
Keywords
Cite
@article{arxiv.1301.2909,
title = {On differentiability of volume time functions},
author = {Piotr T. Chruściel and James D. E. Grant and Ettore Minguzzi},
journal= {arXiv preprint arXiv:1301.2909},
year = {2016}
}
Comments
15 pages, 1 figure; minor corrections, the differentiability proof expanded