期刊
ANNALES HENRI POINCARE
卷 17, 期 10, 页码 2801-2824出版社
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00023-015-0448-3
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资金
- Narodowe Centrum Nauki [DEC-2011/03/B/ST1/02625]
- GNFM of INDAM
- Erwin Schrodinger Institute, Vienna
- Science and Technology Facilities Council [ST/L000490/1] Funding Source: researchfish
- STFC [ST/L000490/1] Funding Source: UKRI
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.
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