Rigidity of parabolic and stable spacelike hypersurfaces in a generalized Robertson–Walker spacetime

Abstract

In this paper, we deal with a parabolic stable spacelike hypersurface immersed in a generalized Robertson–Walker spacetime. We consider the support type function as the product between the warping function and the hyperbolic cosine of the hyperbolic angle of the normal vector field with the timelike parallel direction $$\partial _t$$ . We provide some conditions under which the support type function must be constant or, particularly, when the hypersurface must be a slice, yielding a Calabi–Bernstein type result.