Inextendibility of spacetimes and Lorentzian length spaces

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.

21 pages, 1 figure, made assumptions in 5.4 and 5.6 more explicit (strong causality and local TL geodesic connectedness of extension)

References in corpus (3)

• Causality theory for closed cone structures with applications
• Maximizers in Lipschitz spacetimes are either timelike or null
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