Inextendibility of spacetimes and Lorentzian length spaces
Differential Geometry
2019-11-07 v5 General Relativity and Quantum Cosmology
Mathematical Physics
Metric Geometry
math.MP
Abstract
We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in [KS:17]. To this end, we introduce appropriate notions of geodesics and timelike geodesic completeness and prove a general inextendibility result. Our results shed new light on recent analytic work in this direction and, for the first time, relate low-regularity inextendibility to (synthetic) curvature blow-up.
Keywords
Cite
@article{arxiv.1804.10423,
title = {Inextendibility of spacetimes and Lorentzian length spaces},
author = {James D. E. Grant and Michael Kunzinger and Clemens Sämann},
journal= {arXiv preprint arXiv:1804.10423},
year = {2019}
}
Comments
21 pages, 1 figure, made assumptions in 5.4 and 5.6 more explicit (strong causality and local TL geodesic connectedness of extension)