Obstructions for trapped submanifolds
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909723847032832 |
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| author | Dotti, Gustavo |
| author_facet | Dotti, Gustavo |
| contents | We introduce the concept of $k-$future convex spacelike/null hypersurface $Σ$ in an $n+1$ dimensional spacetime $M$ and prove that no $k-$dimensional closed trapped submanifold (k-CTM) can be tangent to $Σ$ from its future side. As a consequence, k-CTMs cannot be found in open spacetime regions foliated by such hypersurfaces. In gravitational collapse scenarios, specific hypersurfaces of this kind act as past barriers for trapped submanifolds. A number of examples are worked out in detail, two of them showing 3+1 spacetime regions containing trapped loops ($k=1$) but no closed trapped surfaces ($k=2$). The use of trapped loops as an early indicator of black hole formation is briefly discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Obstructions for trapped submanifolds Dotti, Gustavo General Relativity and Quantum Cosmology Differential Geometry We introduce the concept of $k-$future convex spacelike/null hypersurface $Σ$ in an $n+1$ dimensional spacetime $M$ and prove that no $k-$dimensional closed trapped submanifold (k-CTM) can be tangent to $Σ$ from its future side. As a consequence, k-CTMs cannot be found in open spacetime regions foliated by such hypersurfaces. In gravitational collapse scenarios, specific hypersurfaces of this kind act as past barriers for trapped submanifolds. A number of examples are worked out in detail, two of them showing 3+1 spacetime regions containing trapped loops ($k=1$) but no closed trapped surfaces ($k=2$). The use of trapped loops as an early indicator of black hole formation is briefly discussed. |
| title | Obstructions for trapped submanifolds |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2504.01207 |