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/82c68d1d-acb0-4916-b88d-9e75c1dfdd52