Complete Spacelike Hypersurfaces in Generalized Robertson-Walker and the Null Convergence Condition. Calabi-Bernstein problems

TL;DR

This paper investigates constant mean curvature spacelike hypersurfaces in generalized Robertson-Walker spacetimes under null convergence conditions, providing rigidity and Calabi-Bernstein type results especially in Einstein cases.

Contribution

It offers new rigidity theorems and Calabi-Bernstein results for spacelike hypersurfaces in GRW spacetimes satisfying null convergence, including Einstein cases.

Findings

Rigidity results for hypersurfaces under null convergence condition

Calabi-Bernstein type theorems in specific GRW spacetimes

Special focus on Einstein GRW spacetimes

Abstract

We study constant mean curvature spacelike hypersurfaces in generalized Robertson-Walker spacetimes which are spatially parabolic covered (i.e. its fiber F is a (non- compact) complete Riemannian manifold whose universal covering is parabolic) and satisfy the null convergence condition. In particular, we provide several rigidity results under appro- priate mathematical and physical assumptions. We pay special attention to the case where the GRW spacetime is Einstein. As an application, some Calabi-Bernstein type results are given.