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.