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Constant mean curvature foliations of globally hyperbolic spacetimes locally modelled on $AdS_3$

Thierry Barbot·Francois Beguin·Abdelghani Zeghib
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Abstract

We prove that any maximal globally hyperbolic spacetime locally modelled on the anti-de Sitter space of dimension 3, and admitting a closed Cauchy surface, admits a time function $τ$, such that every fiber $τ^{-1}(t)$ is a spacelike surface with constant mean curvature $t$.

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Thierry Barbot, Francois Beguin, Abdelghani Zeghib. 2004-12-06. Constant mean curvature foliations of globally hyperbolic spacetimes locally modelled on $AdS_3$. https://arxiv.org/abs/math/0412111

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