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Main Author: Dotti, Gustavo
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2504.01207
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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