Cauchy hypersurfaces as levels of time and temporal functions

TL;DR

This paper discusses the concept of Cauchy hypersurfaces as levels of time and explores the role of temporal functions in spacetime geometry.

Contribution

It introduces the idea of characterizing Cauchy hypersurfaces as level sets of temporal functions in Lorentzian geometry.

Findings

Cauchy hypersurfaces can be represented as level sets of smooth functions.

Temporal functions provide a natural foliation of spacetime.

The paper's results are incorporated into a newer, clearer publication.

Abstract

This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0507018), in a clearer way.