Maximality of the futures of points in globally hyperbolic maximal conformally flat spacetimes
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914246229491712 |
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| author | Smaï, Rym |
| author_facet | Smaï, Rym |
| contents | Let M be a globally hyperbolic conformally spacetime. We prove that the indecomposable past/future sets (abbrev. IPs/IFs) -in the sense of Penrose, Kronheimer and Geroch -of the universal cover of M are domains of injectivity of the developing map. This relies on the central observation that diamonds are domains of injectivity of the developing map. Using this, we provide a new proof of a result of completeness by C. Rossi, which notably simplifies the original arguments. Furthermore, we establish that if, in addition, M is maximal, the IPs/IFs are maximal as globally hyperbolic conformally flat spacetimes. More precisely, we show that they are conformally equivalent to regular domains of Minkowski spacetime as defined by F. Bonsante. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximality of the futures of points in globally hyperbolic maximal conformally flat spacetimes Smaï, Rym Differential Geometry Mathematical Physics Let M be a globally hyperbolic conformally spacetime. We prove that the indecomposable past/future sets (abbrev. IPs/IFs) -in the sense of Penrose, Kronheimer and Geroch -of the universal cover of M are domains of injectivity of the developing map. This relies on the central observation that diamonds are domains of injectivity of the developing map. Using this, we provide a new proof of a result of completeness by C. Rossi, which notably simplifies the original arguments. Furthermore, we establish that if, in addition, M is maximal, the IPs/IFs are maximal as globally hyperbolic conformally flat spacetimes. More precisely, we show that they are conformally equivalent to regular domains of Minkowski spacetime as defined by F. Bonsante. |
| title | Maximality of the futures of points in globally hyperbolic maximal conformally flat spacetimes |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2501.05856 |