Spacelike hypersurfaces in standard static spacetimes

Abstract

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices, we prove that every complete CMC hypersurface having either bounded hyperbolic angle or bounded height is maximal. Our conclusions follow from general mean curvature estimates for spacelike hypersurfaces. In case where the spacetime is a Lorentzian product with spatial factor of nonnegative Ricci curvature and sectional curvatures bounded below, we also show that a complete maximal hypersurface not intersecting a spacelike slice is itself a slice. This result is obtained from a gradient estimate for parametric maximal hypersurfaces.

arXiv comment50 pages

References in corpus (8)

• The holographic principle
• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Cosmic Holography
• Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
• Calabi-Bernstein results for maximal surfaces in Lorentzian product spaces
• The half-space property and entire positive minimal graphs in M x R
• A note on the uniqueness of global static decompositions
• Uniqueness of static decompositions

Cited by in corpus (1)

• Extremal and weakly trapped submanifolds in Generalized Robertson-Walker spacetimes