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.
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