Obstructions for trapped submanifolds

We introduce the concept of future convex spacelike/null hypersurface Σ in an n + 1 dimensional spacetime M and prove that no 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 (TLs) (k = 1) but no closed trapped surfaces (k = 2). The use of TLs as an early indicator of black hole formation is briefly discussed.