On differentiability of volume time functions

Chruściel, PT, Grant, JDE and Minguzzi, E (2013) On differentiability of volume time functions

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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 :	Authors Email ORCID Chruściel, PT UNSPECIFIED UNSPECIFIED Grant, JDE UNSPECIFIED UNSPECIFIED Minguzzi, E UNSPECIFIED UNSPECIFIED
Date :	14 January 2013
Related URLs :	Author
Additional Information :	Published on arxiv
Depositing User :	Symplectic Elements
Date Deposited :	28 Nov 2014 16:13
Last Modified :	29 May 2015 01:33
URI:	http://epubs.surrey.ac.uk/id/eprint/806578

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