On differentiability of volume time functions

Chruściel, P, Grant, James and Minguzzi, E (2015) On differentiability of volume time functions Annales Henri Poincaré, 17 (10). pp. 2801-2824.

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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.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Name Email ORCID Chruściel, P Grant, James j.grant@surrey.ac.uk Minguzzi, E
Date :	19 December 2015
DOI :	10.1007/s00023-015-0448-3
Copyright Disclaimer :	This is a post-peer-review, pre-copyedit version of an article published in Annales Henri Poincaré. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00023-015-0448-3
Uncontrolled Keywords :	Time Function Conjugate Point Cauchy Hypersurface Causal Curve Global Hyperbolicity
Related URLs :	Author
Depositing User :	Symplectic Elements
Date Deposited :	28 Nov 2014 16:13
Last Modified :	16 Jan 2019 16:54
URI:	http://epubs.surrey.ac.uk/id/eprint/806578

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