
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.
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