r-stable spacelike hypersurfaces in conformally stationary spacetimes

Abstract

In this paper we study the r-stability of closed spacelike hypersurfaces with constant r-th mean curvature in conformally stationary spacetimes of constant sectional curvature. In this setting, we obtain a characterization of r-stability through the analysis of the first eigenvalue of an operator naturally attached to the r-th mean curvature. As an application, we treat the case in which the spacetime is the de Sitter space.