Stability of Spacelike Hypersurfaces in Foliated Spacetimes

Abstract

We show that a given $x:M^n\to {\bar{M}}^{n+1}=I{\times }_{\varphi }{F}^n$ closed spacelike hypersurface with constant mean curvature $H$ and warping function $\varphi$ satisfying ϕ''\geq \ma\{Hϕ'',0\}$iseitherminimaloraspacelikeslice$\{t_{o}\}\times F$forsome$t_{o}\in I$.

10 pages