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The event horizon of a dynamical black hole is generically a non-smoothhypersurface. We classify the types of non-smooth structure that can arise on ahorizon that is smooth at late time. The classification includes creases,corners and caustic points. We prove that creases and corners form spacelikesubmanifolds of dimension $2,1$ and that caustic points form a set of dimensionat most $1$. We classify "perestroikas" of these structures, in which theyundergo a qualitative change at an instant of time. A crease perestroika givesan exact local description of the event horizon near the "instant of merger" ofa generic black hole merger. Other crease perestroikas describe horizonnucleation or collapse of a hole in a toroidal horizon. Caustic perestroikas,in which a pair of caustic points either nucleate or annihilate, provide amechanism for creases to decay. We argue that properties of quantumentanglement entropy suggest that creases might contribute to black holeentropy. We explain that a "Gauss-Bonnet" term in the entropy isnon-topological on a non-smooth horizon, which invalidates previous argumentsagainst such a term.

Creases, corners and caustics: properties of non-smooth structures on black hole horizons