On the global existence of time

TL;DR

This paper investigates the conditions under which a global time function exists in spacetime, showing that its absence implies spacetime singularities using Lorentzian geometry tools.

Contribution

It establishes a link between the non-existence of a global time and the presence of singularities in spacetime under reasonable physical assumptions.

Findings

Absence of a global time implies spacetime singularities.

Uses Lorentzian geometry to analyze global time existence.

Provides conditions under which global time cannot exist.

Abstract

The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I show that, under physically reasonable conditions, the impossibility of finding a global time implies the singularity of spacetime.