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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.02496 |
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| _version_ | 1866913180539682816 |
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| author | Burgos, Saúl Che, Mauricio Prados-Abad, Miguel |
| author_facet | Burgos, Saúl Che, Mauricio Prados-Abad, Miguel |
| contents | We introduce the notion of timelike ideal boundary of a Lorentzian length space as the set of asymptotic classes of future or past-directed timelike geodesic rays, a construction complementary to the causal boundary in the sense of Geroch-Kronheimer-Penrose and akin to the concept of ideal boundary of a metric space. We endow such a timelike ideal boundary with a natural cone topology and an angular metric, and establish upper curvature bounds for the resulting metric space. Finally, we consider generalized cones as a model and study the relation between the timelike ideal boundary and both the metric ideal boundary of the fiber and the asymptotic behaviour of the warping function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02496 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Timelike ideal boundary of non-positively curved Lorentzian spaces Burgos, Saúl Che, Mauricio Prados-Abad, Miguel Metric Geometry Mathematical Physics Differential Geometry 51K10, 53B30, 53C23, 53C50 We introduce the notion of timelike ideal boundary of a Lorentzian length space as the set of asymptotic classes of future or past-directed timelike geodesic rays, a construction complementary to the causal boundary in the sense of Geroch-Kronheimer-Penrose and akin to the concept of ideal boundary of a metric space. We endow such a timelike ideal boundary with a natural cone topology and an angular metric, and establish upper curvature bounds for the resulting metric space. Finally, we consider generalized cones as a model and study the relation between the timelike ideal boundary and both the metric ideal boundary of the fiber and the asymptotic behaviour of the warping function. |
| title | Timelike ideal boundary of non-positively curved Lorentzian spaces |
| topic | Metric Geometry Mathematical Physics Differential Geometry 51K10, 53B30, 53C23, 53C50 |
| url | https://arxiv.org/abs/2606.02496 |