Obstructions for trapped submanifolds

Gustavo Dotti

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arXiv · 2504.01207

Obstructions for trapped submanifolds

Gustavo Dotti

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Abstract

We introduce the concept of $k-$future convex spacelike/null hypersurface $\Sigma$ in an $n+1$ dimensional spacetime $M$ and prove that no $k-$dimensional closed trapped submanifold (k-CTM) can be tangent to $\Sigma$ 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.

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Gustavo Dotti. 2025-04-01. Obstructions for trapped submanifolds. https://arxiv.org/abs/2504.01207

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