论文标题
具有非负时间曲率的全球双曲线洛伦兹长度空间的分裂定理
The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature
论文作者
论文摘要
在这项工作中，我们证明了一个合成的分裂定理，用于全球双曲线Lorentzian长度空间，其全球非负时间曲率曲率包含完整的时光型线。就像在平稳的空间时一样，我们构建完整的时脉络渐近线，通过三角比较，可以证明可以将其融合在一起以提供时间表式线。为了控制他们的行为，我们本着亚历山德罗夫空间的分裂定理的精神介绍了平行线的平行性概念，并表明渐近线都是平行的。这有助于建立给定线路的社区。然后，我们证明该社区具有及时的完整性属性，因此是不可扩展性的，它全球范围是本地结果。
In this work, we prove a synthetic splitting theorem for globally hyperbolic Lorentzian length spaces with global non-negative timelike curvature containing a complete timelike line. Just like in the case of smooth spacetimes, we construct complete, timelike asymptotes which, via triangle comparison, can be shown to fit together to give timelike lines. To get a control on their behaviour, we introduce the notion of parallelity of timelike lines in the spirit of the splitting theorem for Alexandrov spaces and show that asymptotic lines are all parallel. This helps to establish a splitting of a neighbourhood of the given line. We then show that this neighbourhood has the timelike completeness property and is hence inextendible, which globalises the local result.
