Timelike Completeness as an Obstruction to C 0-Extensions
Timelike Completeness as an Obstruction to C 0-Extensions
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DOI：
10.1007/s00220-017-3019-2
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发表时间：
2018-05-01
影响因子：
2.4
通讯作者：
Sbierski, Jan
中科院分区：
文献类型：
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作者：
Galloway, Gregory J.;Ling, Eric;Sbierski, Jan
洛伦兹流形的低正则(In-)可扩性的研究是由爱因斯坦方程的一个给定解是否可以扩展(或极大)为弱解的问题所推动的。本文证明了类时完备整体双曲洛伦兹流形是C(0)-不可扩张的。为了证明，我们利用Samann(Ann Henri Poincar，17(6)：1429-1455,2016)最近建立的结果，即即使对于全局双曲的连续洛伦兹流形，在任意两个因果相关点之间也存在长度最大化的因果曲线。
The study of low regularity (in-)extendibility of Lorentzian manifolds is motivated by the question whether a given solution to the Einstein equations can be extended (or is maximal) as a weak solution. In this paper we show that a timelike complete and globally hyperbolic Lorentzian manifold is C (0)-inextendible. For the proof we make use of the result, recently established by Samann (Ann Henri Poincar, 17(6):1429-1455, 2016), that even for continuous Lorentzian manifolds that are globally hyperbolic, there exists a length-maximizing causal curve between any two causally related points.