  We examine the wave-functionals describing the collapse of a self-gravitating
dust ball in an exact quantization of the gravity-dust system. We show that
ingoing (collapsing) dust shell modes outside the apparent horizon must
necessarily be accompanied by outgoing modes inside the apparent horizon, whose
amplitude is suppressed by the square root of the Boltzmann factor at the
Hawking temperature. Likewise, ingoing modes in the interior must be
accompanied by outgoing modes in the exterior, again with an amplitude
suppressed by the same factor. A suitable superposition of the two solutions is
necessary to conserve the dust probability flux across the apparent horizon,
thus each region contains both ingoing and outgoing dust modes. If one
restricts oneself to considering only the modes outside the apparent horizon
then one should think of the apparent horizon as a partial reflector, the
probability for a shell to reflect being given by the Boltzmann factor at the
Hawking temperature determined by the mass contained within it. However, if one
considers the entire wave function, the outgoing wave in the exterior is seen
to be the transmission through the horizon of the interior outgoing wave that
accompanies the collapsing shells. This transmission could allow information
from the interior to be transferred to the exterior.
