论文标题
真空空间中紧凑型cauchy视野的分类定理
A classification theorem for compact Cauchy horizons in vacuum spacetimes
论文作者
论文摘要
我们为拓扑结构建立了一个完整的分类定理，并为紧凑的非脱位库奇（Cauchy Horizons of Time Ablesiable Ablesistion flase tocientime $ 3+1 $ -Spactime）建立了无效的非排分cauchy Horizons的无效发电机。我们表明，要么：（i）所有发电机均关闭，要么（ii）仅关闭两个发电机，任何其他任何发电机都填充了两个折叠，或者（iii）每个发电机密集地填充了两个托和（iv）每个发电机密集地填充地平线。然后，我们证明（i） - （iv）分别是：（i'）seifert歧管，或（ii'）镜头空间，或（iii'）在一个圆圈上的两个螺栓束，或者（iv'）三折。示例中已知所有四种可能性都会出现。在最后一个情况下，（iv），（iv'），我们还表明，时空确实是扁平的，因此解决了Isenberg和Moncrief在Ergodic Horizons中提出的问题。本文的结果为所有真空空间的指标与紧凑的cauchy地平线进行了全面参数化。证明方法允许直接概括更高的维度。
We establish a complete classification theorem for the topology and for the null generators of compact non-degenerate Cauchy horizons of time orientable smooth vacuum $3+1$-spacetimes. We show that, either: (i) all generators are closed, or (ii) only two generators are closed and any other densely fills a two-torus, or (iii) every generator densely fills a two-torus, or (iv) every generator densely fills the horizon. We then show that, respectively to (i)-(iv), the horizon's manifold is either: (i') a Seifert manifold, or (ii') a lens space, or (iii') a two-torus bundle over a circle, or, (iv') a three-torus. All the four possibilities are known to arise in examples. In the last case, (iv), (iv'), we show in addition that the spacetime is indeed flat Kasner, thus settling a problem posed by Isenberg and Moncrief for ergodic horizons. The results of this article open the door for a full parameterization of the metrics of all vacuum spacetimes with a compact Cauchy horizon. The method of proof permits direct generalizations to higher dimensions.
