Gustavo Dotti: Obstructions for trapped submanifolds

Tuesday Jun 17, 2025, 10:30 AM → 11:30 AM Europe/Paris

We introduce the concept of $k$−future convex spacelike/null hypersurface $\Sigma$ in an $n + 1$ dimensional spacetime and prove that no $k$−dimensional trapped submanifold can be tangent to $\Sigma$ from its future side. As a consequence, $k$-dimensional closed trapped submanifolds 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. Examples will be given of (3+1) spacetime regions containing trapped loops ($k = 1$) but no closed trapped surfaces ($k = 2$) and of how trapped loops could be used as an early indicator of black hole formation in numerical relativity.