Special temporal functions on globally hyperbolic manifolds

TL;DR

This paper investigates the existence of special temporal functions on globally hyperbolic manifolds, focusing on bounds on geometric quantities and their relation to completeness and embeddings in Minkowski space.

Contribution

It provides new existence results for temporal functions with specific geometric bounds on globally hyperbolic manifolds, connecting to completeness and isometric embeddings.

Findings

Existence of temporal functions with bounds on lapse and shift.

Connections between geometric bounds and completeness.

Results on isometric embeddings in Minkowski space.

Abstract

In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are linked to completeness properties and the existence of closed isometric embeddings in Minkowski spaces.