On Differentiability of Volume Time Functions

Author(s)
Piotr T. Chrusciel, James D. E. Grant, Ettore Minguzzi
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 space-times Hawking's time function can be uniformly approximated by smooth time functions with timelike gradient.

Organisation(s)
Gravitational Physics
External organisation(s)
University of Surrey, University of Florence
Journal
Annales Henri Poincare
Volume
17
Pages
2801-2824
No. of pages
24
ISSN
1424-0637
DOI
https://doi.org/10.1007/s00023-015-0448-3
Publication date
10-2016
Peer reviewed
Yes
Austrian Fields of Science 2012
103028 Theory of relativity, 103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Nuclear and High Energy Physics, Statistical and Nonlinear Physics, Mathematical Physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/on-differentiability-of-volume-time-functions(82c68d1d-acb0-4916-b88d-9e75c1dfdd52).html