论文标题
通过无效距离的眼睛的全球双曲线
Global Hyperbolicity through the Eyes of the Null Distance
论文作者
论文摘要
Lorentzian几何形状中没有Hopf-Rinow定理。尽管如此，我们证明，只有与时间函数的无距离进行指标完成时，时空是全球双曲线的。我们的方法基于这样的观察，即无效距离在规律性和因果关系方面对于弱的时间功能特别好。具体而言，我们还表明，凯奇时间函数和常规宇宙学时间函数的零距离在全球范围内编码因果关系。
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on the observation that null distances behave particularly well for weak temporal functions in terms of regularity and causality. Specifically, we also show that the null distances of Cauchy temporal functions and regular cosmological time functions encode causality globally.
