Abstract
What do the typical entangled states of two black holes look like? Do they
contain firewalls? We approach these questions constructively, providing
ensembles of states which densely explore the black hole Hilbert space. None of
the states contain firewalls. On the contrary, they contain very long
Einstein-Rosen (ER) caterpillars: wormholes with large numbers of matter
inhomogeneities. Distinguishing these ensembles from the typical entangled
states of the black holes is hard. We quantify this by deriving the
correspondence between a microscopic notion of quantum randomness and the
geometric length of the wormhole. This formalizes a "complexity = geometry''
relation.