On the $r-$stability of spacelike hypersurfaces

TL;DR

This paper investigates the strong stability of spacelike hypersurfaces with constant r-th mean curvature within specific curved spacetimes, including de Sitter space, contributing to the understanding of geometric stability in general relativity.

Contribution

It provides new results on the strong stability of r-th mean curvature hypersurfaces in generalized Robertson-Walker spacetimes, especially in de Sitter space.

Findings

Established conditions for strong stability of hypersurfaces with constant r-th mean curvature.

Extended stability analysis to spacetimes of constant sectional curvature.

Applied results specifically to the de Sitter space case.

Abstract

In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient spacetime is the de Sitter space.