关于全球超曲性概念的最新进展
Recent progress on the notion of global hyperbolicity
AI总结：
本文综述了全球超曲性概念的不同方法，包括经典方法和最新结果，探讨了因果曲线、嵌入性及修正的因果和共形边界。
摘要：
全球超曲性是数学相对论中的核心概念。本文回顾了这一概念的不同方法，解释了经典方法和最新结果。前者包括Cauchy超曲面、裸奇点和连接两个事件的因果曲线。后者包括对全球超曲时空的结构结果、其在洛伦兹-闵氏空间中的嵌入性，以及最近修正的因果和共形边界概念。此外，还回顾了两个检查全球超曲性的标准。第一个适用于一般分裂时空，第二个则以自然关联的Finsler度量形式准确刻画了全球超曲性和类空Cauchy超曲面的标准 stationary 时空。
英文摘要：
Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked singularities, and the space of the causal curves connecting two events. The latter includes structural results on globally hyperbolic spacetimes, their embeddability in Lorentz-Minkowski, and the recently revised notions of both, causal and conformal boundaries. Moreover, two criteria for checking global hyperbolicity are reviewed. The first one applies to general splitting spacetimes. The second one characterizes accurately global hyperbolicity and spacelike Cauchy hypersurfaces for standard stationary spacetimes, in terms of a naturally associated Finsler metric.
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