Creases, corners, and caustics: Properties of nonsmooth structures on black hole horizons

Abstract

The event horizon of a dynamical black hole is generically a nonsmooth hypersurface. We classify the types of nonsmooth structure that can arise on a horizon that is smooth at late time. The classification includes creases, corners and caustic points. We prove that creases and corners form spacelike submanifolds of dimension 2,1 and that caustic points form a set of dimension at most 1. We classify “perestroikas” of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an exact local description of the event horizon near the “instant of merger” of a generic black hole merger. Other crease perestroikas describe horizon nucleation or collapse of a hole in a toroidal horizon. Caustic perestroikas, in which a pair of caustic points either nucleate or annihilate, provide a mechanism for creases to decay. We argue that properties of quantum entanglement entropy suggest that creases might contribute to black hole entropy. We explain that a “Gauss-Bonnet” term in the entropy is nontopological on a nonsmooth horizon, which invalidates previous arguments against such a term.