Concavity of spacetimes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912923792703488 |
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| author | Beran, Tobias Erös, Darius Ohta, Shin-ichi Rott, Felix |
| author_facet | Beran, Tobias Erös, Darius Ohta, Shin-ichi Rott, Felix |
| contents | Motivated by recent breathtaking progress in the synthetic study of Lorentzian geometry, we investigate the local concavity of time separation functions on Finsler spacetimes as a Lorentzian counterpart to Busemann's convexity in metric geometry. We show that a Berwald spacetime is locally concave if and only if its flag curvature is nonnegative in timelike directions. We also give another characterization of nonnegative flag curvature by the convexity of future (or past) capsules, inspired by Kristály--Kozma's result in the positive definite case. These characterizations are new even for Lorentzian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concavity of spacetimes Beran, Tobias Erös, Darius Ohta, Shin-ichi Rott, Felix Differential Geometry Mathematical Physics 53B30, 53C50, 53C60 Motivated by recent breathtaking progress in the synthetic study of Lorentzian geometry, we investigate the local concavity of time separation functions on Finsler spacetimes as a Lorentzian counterpart to Busemann's convexity in metric geometry. We show that a Berwald spacetime is locally concave if and only if its flag curvature is nonnegative in timelike directions. We also give another characterization of nonnegative flag curvature by the convexity of future (or past) capsules, inspired by Kristály--Kozma's result in the positive definite case. These characterizations are new even for Lorentzian manifolds. |
| title | Concavity of spacetimes |
| topic | Differential Geometry Mathematical Physics 53B30, 53C50, 53C60 |
| url | https://arxiv.org/abs/2509.26196 |