  Recently, Almheiri et. al. argued, via a delicate thought experiment, that it
is not consistent to simultaneosuly require that (a) Hawking radiation is pure,
(b) effective field theory is valid outside a stretched horizon and (c)
infalling observers encounter nothing unusual as they cross the horizon. These
are the three fundamental assumptions underlying Black Hole Complementarity and
the authors proposed that the most conservative resolution of the paradox is
that (c) is false and the infalling observer burns up at the horizon (the
horizon acts as a "firewall"). However, the firewall violates the equivalence
principle and breaks the CPT invariance of quantum gravity. This led Hawking to
propose recently that gravitational collapse may not end up producing event
horizons, although he did not give a mechanism for how this may happen. Here we
will support Hawking's conclusion in a quantum gravitational model of dust
collapse. We will show that continued collapse to a singularity can only be
achieved by combining two independent and entire solutions of the
Wheeler-DeWitt equation. We interpret the paradox as simply forbidding such a
combination, which leads naturally to a picture in which matter condenses on
the apparent horizon during quantum collapse.
