具有常非零表面引力的紧致 Cauchy 视界的真空时空的对称性
Symmetries of vacuum spacetimes with a compact Cauchy horizon of constant non-zero surface gravity
AI总结：
本文证明含可归一化为非零常数表面引力的紧致 Cauchy 视界的光滑真空时空必存在 Killing 向量场，支持强宇宙监督猜想。
摘要：
我们证明，任何光滑真空时空若包含一个紧致 Cauchy 视界，且其表面引力可归一化为非零常数，则该时空容许一个 Killing 向量场。这就在关于表面引力的假设下证明了 Moncrief 和 Isenberg 于 1983 年提出的一个猜想，并推广了 Moncrief-Isenberg 以及 Friedrich-Rácz-Wald 先前的结果；在那些结果中，Cauchy 视界的生成元是闭合的，或者稠密地充满一个二维环面。因此，一般初始数据的最大全局双曲真空发展不能穿过一个表面引力可归一化为非零常数的紧致 Cauchy 视界进行延拓。由此，我们的结果在所考虑的特殊情形下支持了强宇宙监督猜想的有效性。证明由两个主要步骤组成。首先，我们证明 Killing 方程可以在 Cauchy 视界处求解至无穷阶。其次，通过应用第一作者近期关于在紧致 Cauchy 视界上给定初始数据的波动方程的结果，我们证明这个 Killing 向量场可以延拓到全局双曲区域。
英文摘要：
We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This proves a conjecture by Moncrief and Isenberg from 1983 under the assumption on the surface gravity and generalises previous results due to Moncrief-Isenberg and Friedrich-Rácz-Wald, where the generators of the Cauchy horizon were closed or densely filled a 2-torus. Consequently, the maximal globally hyperbolic vacuum development of generic initial data cannot be extended across a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant. Our result supports, thereby, the validity of the strong cosmic censorship conjecture in the considered special case. The proof consists of two main steps. First, we show that the Killing equation can be solved up to infinite order at the Cauchy horizon. Second, by applying a recent result of the first author on wave equations with initial data on a compact Cauchy horizon, we show that this Killing vector field extends to the globally hyperbolic region.
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。
