A note on invariant temporal functions

TL;DR

This paper proves the existence of invariant Cauchy temporal functions in globally hyperbolic manifolds under compact conformal group actions, unifying previous results into a comprehensive theorem.

Contribution

It establishes a general theorem on invariant Cauchy temporal functions, extending and unifying prior results without requiring prior Lorentzian geometry knowledge.

Findings

Existence of invariant Cauchy temporal functions proven

Unified previous results into a comprehensive theorem

Applicable to arbitrary globally hyperbolic manifolds

Abstract

The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous results about the existence of Cauchy temporal functions with additional properties on arbitrary globally hyperbolic manifolds are unified in a fully general theorem. The article is written as self-contained as possible, no prior knowledge on Lorentzian geometry is assumed.