Curvature bounds, regularity and inextendibility of spacetimes
General Relativity and Quantum Cosmology
2026-03-24 v1 Mathematical Physics
Differential Geometry
Metric Geometry
math.MP
Abstract
We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This enables us to relate low-regularity inextendibility of spacetimes to unboundedness of curvature - which is at present unattainable using classical methods - thereby strengthening and complementing the results of Grant-Kunzinger-Saemann (2019) significantly.
Cite
@article{arxiv.2603.20802,
title = {Curvature bounds, regularity and inextendibility of spacetimes},
author = {Tobias Beran and John Harvey and Clemens Sämann},
journal= {arXiv preprint arXiv:2603.20802},
year = {2026}
}
Comments
16 pages, 2 figures