Refocusing spacetimes need not be strongly refocusing
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917518299365376 |
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| author | Bauermeister, Friedrich |
| author_facet | Bauermeister, Friedrich |
| contents | We prove that there are globally hyperbolic spacetimes $(X,g)$ which are refocusing but not strongly refocusing. In fact, every globally hyperbolic strongly refocusing spacetime of dimension at least $3$ admits globally hyperbolic metrics which are refocusing but not strongly refocusing. This answers a question by Chernov, Kinlaw, and Sadykov. We then prove that globally hyperbolic spacetimes which are Legendrian refocusing (a notion introduced in this paper) admit globally hyperbolic strongly refocusing metrics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refocusing spacetimes need not be strongly refocusing Bauermeister, Friedrich Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53C50 (Primary) 53C22, 58D17 (Secondary) We prove that there are globally hyperbolic spacetimes $(X,g)$ which are refocusing but not strongly refocusing. In fact, every globally hyperbolic strongly refocusing spacetime of dimension at least $3$ admits globally hyperbolic metrics which are refocusing but not strongly refocusing. This answers a question by Chernov, Kinlaw, and Sadykov. We then prove that globally hyperbolic spacetimes which are Legendrian refocusing (a notion introduced in this paper) admit globally hyperbolic strongly refocusing metrics. |
| title | Refocusing spacetimes need not be strongly refocusing |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53C50 (Primary) 53C22, 58D17 (Secondary) |
| url | https://arxiv.org/abs/2605.21871 |