At the end of the world: Local Dynamical Cobordism

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions Einstein gravity coupled to scalars containing such end-of-the-world "branes". latter appear in effective theory singularity finite distance which go off infinite field space distance. provide local description near branes, simplify dramatically and are characterized terms critical exponent, controls asymptotic profiles fields universal scaling relations among singularity, distance, curvature. analysis does not rely on supersymmetry. many explicit examples Local Dynamical Cobordisms string theory, including 10d massive IIA, non-supersymmetric $USp(32)$ Bubbles Nothing, 4d $ \mathcal{N}=1 cosmic solutions, Klebanov-Strassler throat, D$p$-brane brane configurations related D1/D5 systems, small black holes. Our framework encompasses diverse recent setups diverge core defects, by regarding them suitable branes. explore interplay with Distance other swampland constraints.