arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2103.13157gr-qcmath-phmath.MP
收藏

时序空间的一个时间分裂定理

A Temporal Splitting Theorem for Chronological Spaces

Faculty of Sciences (I), Lebanese University（黎巴嫩大学理学院（一））

Ali Bleybel

备注：
24 pages, 3 figures. Substantially revised and expanded. New proof of the discrete antichain-extension result; the earlier compatibility proposition is omitted. The continuum construction is replaced by a direct past-set argument. Includes temporal splitting for chronological spaces under explicit hypotheses and a separate generalized Cauchy-hypersurface theorem
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文在拓扑与序条件下将Geroch时间叶状定理推广至时序空间，证明可构造含给定反链的叶状结构，并证得时序时空存在含指定紧致非时序集的广义Cauchy超曲面。

摘要：

我们在适当的拓扑和序理论条件下，将Geroch关于全局双曲时空中的时间叶状结构定理推广到时序空间。该叶状结构可以被选择为包含一个给定的相对紧致反链于某一层中。我们首先证明可数因果集的相应推广结果，然后利用过去集对时序空间给出直接证明。此外，我们证明任何时序时空都承认一个包含指定紧致非时序集的广义Cauchy超曲面：每条不可延拓的类时曲线（同时也是极大时序链）都恰好穿过该超曲面一次。

英文摘要：

We obtain a generalization of Geroch's Theorem on temporal foliations in a globally hyperbolic space-time to chronological spaces under suitable topological and order-theoretic requirements. The foliation can be chosen to contain a given relatively compact antichain in one slice. We first prove the corresponding extension result for countable causal sets, and then give a direct proof for chronological spaces using past sets. Furthermore, we show that any chronological space-time admits a generalized Cauchy hypersurface containing a prescribed compact achronal set: it is crossed once by every inextendible timelike curve which is also a maximal chronological chain.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑