A note on the uniqueness of global static decompositions

Abstract

We discuss when static Killing vector fields are standard, that is, leading to a global orthogonal splitting of the spacetime. We prove that such an orthogonal splitting is unique whenever the natural space is compact. This is carried out by proving that many notable spacelike submanifolds must be contained in an orthogonal slice. Possible obstructions to the global splitting are also considered.

6 pages, no figures

References in corpus (6)

• On smooth Cauchy hypersurfaces and Geroch's splitting theorem
• Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions
• Trapped surfaces and symmetries
• On completeness of orbits of Killing vector fields
• Ricci Fall-off in Static, Globally Hyperbolic, Non-singular Spacetimes
• A note on static metrics

Cited by in corpus (4)

• A note on the existence of standard splittings for conformally stationary spacetimes
• Standard static Finsler spacetimes
• Spacelike hypersurfaces in standard static spacetimes
• Uniqueness of static decompositions