Trans-Planckian censorship and spacetime singularities

TL;DR

This paper explores how the trans-planckian censorship conjecture (TCC) influences the geodesic completeness of spacetime, providing conditions that prevent singularities and ensure infinite proper time evolution.

Contribution

It establishes a link between TCC bounds and geodesic completeness, deriving criteria for non-singular spacetime evolution using mathematical tools like Gronwall's lemma.

Findings

TCC bounds imply the absence of blowup solutions in spacetime.

Bounded extrinsic curvature is necessary for geodesic completeness.

Results are relevant for classical evolution of Friedmann universes.

Abstract

We study the effects of trans-planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall's lemma, TCC bounds can be derived directly, leading to a result about the absence of blowup solutions. We show that the TCC provides part of the required criteria for geodesic completeness, and we then provide the remaining ones - the norm of the extrinsic curvature being bounded away from zero. We also discuss the importance of these results for the classical evolution of Friedmann universes under the assumptions of global and regular hyperbolicity.