  Quantum gravity suggests that the paradox recently put forward by Almheiri
et. al. (AMPS) can be resolved if matter does not undergo continuous collapse
to a singularity but condenses on the apparent horizon. One can then expect a
quasi-static object to form even after the gravitational field has overcome any
degeneracy pressure of the matter fields. We consider dust collapse. If the
collapse terminates on the apparent horizon, the Misner-Sharp mass function of
the dust ball is predicted and we construct static solutions with no tangential
pressure that would represent such a compact object. The collapse wave
functions indicate that there will be processes by which energy extraction from
the center occurs. These leave behind a negative point mass at the center which
contributes to the total energy of the system but has no effect on the the
energy density of the dust ball. The solutions describe a compact object whose
boundary lies outside its Schwarzschild radius and which is hardly
distinguishable from a neutron star.
