Stability of Spacelike Hypersurfaces in Foliated Spacetimes

We show that a given $x:M^n\to \bar{M}^{n+1}=I\times_{\phi}F^{n}$ closed spacelike hypersurface with constant mean curvature $H$ and warping function $\phi$ satisfying \phi ''\geq \ma\{H\phi'',0\}$ is either minimal or a spacelike slice $\{t_{o}\}\times F$ for some $t_{o}\in I$.