论文标题
有关因果关系条件的注释
A note on causality conditions on covering spacetimes
论文作者
论文摘要
Lorentzian几何形状中的许多技术，例如在奇异定理证明中使用的技术，取决于某些平滑覆盖物保留了有趣的全球几何特性，包括因果关系。在本说明中，我们给出了明确的例子，表明，与因果阶梯的某些更常见的因果关系或全球性增压性，诸如因果的连续性或因果关系较少的条件（例如，一般而言）掩盖的条件（如作者（em）所猜测）。结果，必须对这些因果关系条件转移到掩护的任何结果进行相应修改。特别是，这里还介绍了我们一个人（IPC）先前给出的gannon-lee奇异定理的声明和证明中的一些修正案，以解决其原始证明中的差距。
A number of techniques in Lorentzian geometry, such as those used in the proofs of singularity theorems, depend on certain smooth coverings retaining interesting global geometric properties, including causal ones. In this note we give explicit examples showing that, unlike some of the more commonly adopted rungs of the causal ladder such as strong causality or global hyperbolicity, less-utilized conditions such as causal continuity or causal simplicity do not in general pass to coverings, as already speculated by one of the authors (EM). As a consequence, any result which relies on these causality conditions transferring to coverings must be revised accordingly. In particular, some amendments in the statement and proof of a version of the Gannon-Lee singularity theorem previously given by one of us (IPCS) are also presented here that address a gap in its original proof.
