Global Hyperbolicity through the Eyes of the Null Distance
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910396790603776 |
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| author | Burtscher, Annegret García-Heveling, Leonardo |
| author_facet | Burtscher, Annegret García-Heveling, Leonardo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_15610 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global Hyperbolicity through the Eyes of the Null Distance Burtscher, Annegret García-Heveling, Leonardo Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Metric Geometry 53C50 (Primary), 53C23, 53B30, 83C05 (Secondary) 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. |
| title | Global Hyperbolicity through the Eyes of the Null Distance |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics Metric Geometry 53C50 (Primary), 53C23, 53B30, 83C05 (Secondary) |
| url | https://arxiv.org/abs/2209.15610 |