  The formation and evaporation of small AdS black holes in a theory with a
holographic dual is governed by the usual rules of quantum mechanics. The
eigenstate thermalization hypothesis explains the validity of semiclassical
gravity for local bulk observables and can be used to quantify the magnitude of
quantum corrections to the semiclassical approximation. The holographic dual
produces a basis of black hole states with finite energy width, and observables
that are smooth functions on the classical phase space will self-average over a
large number of energy eigenstates, exponential in the Bekenstein-Hawking
entropy S, leading to results that are consistent with semiclassical gravity up
to small corrections of order exp(-S/2). As expected, the semiclassical
description breaks down for transition amplitudes that contribute to the
unitary S matrix of the holographic theory.
