The stability of closed linear Weingarten spacelike hypersurfaces in foliated spacetimes

Abstract

This paper discusses the stability concerning closed linear Weingarten spacelike hypersurfaces [Formula: see text] immersed in foliated spacetimes. Firstly, we show that a totally umbilic [Formula: see text] is strongly stable. Secondly, given a generalized Robertson–Walker spacetime [Formula: see text] whose warping function [Formula: see text] is under a suitable restriction, we prove that if [Formula: see text] is strongly stable, then it is totally umbilic.