The paper “On differentiability of volume time functions” co-authored by Piotr Chrusciel (Vienna), James Grant, and Ettore Minguzzi (Firenze) has been accepted for publication by the Annales Henri Poincare.  The online version at Springer is here and the arXiv version is here.  The paper shows differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, they 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, they prove that in stably causal spacetimes Hawking’s time function can be uniformly approximated by smooth time functions with timelike gradient.