Uniqueness of static decompositions

Abstract

We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warping function satisfies severe restrictions, leading us to our classification results. Moreover, we show that certain condition on the lightlike sectional curvature ensures the uniqueness of static decomposition for Lorentzian manifolds.

14 pages

References in corpus (3)

• Global decomposition of a Lorentzian manifold as a Generalized Robertson-Walker space
• A note on the uniqueness of global static decompositions
• Semi-Riemannian manifolds with a doubly warped structure

Cited by in corpus (1)

• Spacelike hypersurfaces in standard static spacetimes