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