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 | ||||||||||||
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Divisions : | Faculty of Engineering and Physical Sciences > Mathematics | ||||||||||||
Authors : |
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Date : | 19 December 2015 | ||||||||||||
Identification Number : | 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 | ||||||||||||
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Depositing User : | Symplectic Elements | ||||||||||||
Date Deposited : | 28 Nov 2014 16:13 | ||||||||||||
Last Modified : | 17 Apr 2018 10:06 | ||||||||||||
URI: | http://epubs.surrey.ac.uk/id/eprint/806578 |
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