Global Hyperbolicity through the Eyes of the Null Distance
arXiv:2209.15610 · doi:10.1007/s00220-024-04936-5
Abstract
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.
arXiv commentSmall corrections compared to v3. Final version. 36 pages, 4 figures
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