A synthetic Gannon-Lee incompleteness theorem
General Relativity and Quantum Cosmology
2026-02-17 v1 Mathematical Physics
Differential Geometry
Metric Geometry
math.MP
Abstract
We prove the Gannon-Lee incompleteness theorem for globally hyperbolic spacetimes. We assume the synthetic null energy condition of Ketterer and a trappedness condition we call "synthetically asymptotically regular". Our result generalizes this classical result to the weighted case. It also motivates and indicates extensions to low regularity, which are deferred to future work.
Keywords
Cite
@article{arxiv.2602.14246,
title = {A synthetic Gannon-Lee incompleteness theorem},
author = {Mathias Braun and Carlo Rotolo},
journal= {arXiv preprint arXiv:2602.14246},
year = {2026}
}
Comments
20 pages. Comments welcome