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

Barbot, Thierry; Beguin, Francois; Zeghib, Abdelghani

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

Authors

Barbot, Thierry

Beguin, Francois

Zeghib, Abdelghani

Description

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 $t$.