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Annales Henri Poincaré

, Volume 17, Issue 10, pp 2801–2824 | Cite as

On Differentiability of Volume Time Functions

  • Piotr T. ChruścielEmail author
  • James D. E. Grant
  • Ettore Minguzzi
Article

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 space-times Hawking’s time function can be uniformly approximated by smooth time functions with timelike gradient.

Keywords

Time Function Conjugate Point Cauchy Hypersurface Causal Curve Global Hyperbolicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing 2015

Authors and Affiliations

  • Piotr T. Chruściel
    • 1
    Email author
  • James D. E. Grant
    • 2
  • Ettore Minguzzi
    • 3
  1. 1.Fakultät für Physik and Erwin Schrödinger InstituteUniversität WienWienAustria
  2. 2.Department of Mathematics, Faculty of Engineering and Physical SciencesUniversity of SurreyGuildfordUK
  3. 3.Dipartimento di Matematica e Informatica “U. Dini”Università degli Studi di FirenzeFlorenceItaly

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