2025/04/01 by Dotti, Gustavo · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2504.01207
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.