Grant James D E, Kunzinger Michael, Sämann Clemens
1Department of Mathematics, University of Surrey, Guildford, UK.
2Faculty of Mathematics, University of Vienna, Vienna, Austria.
Ann Glob Anal Geom (Dordr). 2019;55(1):133-147. doi: 10.1007/s10455-018-9637-x. Epub 2018 Nov 10.
We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in Kunzinger and Sämann (Ann Glob Anal Geom 54(3):399-447, 2018). 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.
我们在Kunzinger和Sämann（《全局分析与几何学年鉴》54(3):399 - 447, 2018）所发展的洛伦兹长度空间的综合几何框架内，研究时空的低正则性（非）可扩展性。为此，我们引入了测地线和类时测地线完备性的适当概念，并证明了一个一般性的不可扩展性结果。我们的结果为该方向上最近的分析工作提供了新的思路，并且首次将低正则性不可扩展性与（综合）曲率爆破联系起来。
