Inextendibility of spacetimes and Lorentzian length spaces

TL;DR

This paper investigates the inextendibility of low-regularity spacetimes using Lorentzian length spaces, establishing a connection between inextendibility and synthetic curvature blow-up, and providing new insights into the geometric structure of such spacetimes.

Contribution

It introduces notions of geodesics and timelike geodesic completeness in Lorentzian length spaces and proves a general inextendibility result linking low-regularity to curvature blow-up.

Findings

Established a general inextendibility theorem for low-regularity spacetimes.

Connected inextendibility to synthetic curvature blow-up.

Provided new geometric insights into 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.