2013/01/31 by Piotr T. Chruściel, James D. E. Grant, Ettore Minguzzi · 2 citations
Mathematics · Physics and Astronomy · #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1007/s00023-015-0448-3
published as Annales Henri Poincaré 17 (2016), 2801-2824 · 15 pages, 1 figure; minor corrections, the differentiability proof expanded
arxiv created 2015/11/01 · arxiv updated 2016/12/02
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.