Conformal transformations of spacetimes without observer horizons
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913842143952896 |
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| author | García-Heveling, Leonardo Zeghib, Abdelghani |
| author_facet | García-Heveling, Leonardo Zeghib, Abdelghani |
| contents | We prove that for a certain class of Lorentzian manifolds, namely causal spacetimes without observer horizons, conformal transformations can be classified into two types: escaping and non-escaping. This means that successive powers of a given conformal transformation will either send all points to infinity, or none. As an application, we classify the conformal transformations of Einstein's static universe. We also study the question of essentiality in this context, i.e. which conformal transformations are isometric for some metric in the conformal class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal transformations of spacetimes without observer horizons García-Heveling, Leonardo Zeghib, Abdelghani Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53C50 (primary) 58D19 (secondary) We prove that for a certain class of Lorentzian manifolds, namely causal spacetimes without observer horizons, conformal transformations can be classified into two types: escaping and non-escaping. This means that successive powers of a given conformal transformation will either send all points to infinity, or none. As an application, we classify the conformal transformations of Einstein's static universe. We also study the question of essentiality in this context, i.e. which conformal transformations are isometric for some metric in the conformal class. |
| title | Conformal transformations of spacetimes without observer horizons |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 53C50 (primary) 58D19 (secondary) |
| url | https://arxiv.org/abs/2505.11148 |