  We describe the ground state for a gravitationally collapsed ball of dust as
the direct product of wavefunctions for dust particles distributed over an
arbitrary number of nested layers. This allows us to estimate the expectation
value of the global radius as well as the effective energy density and
pressures for the dust core of quantum black holes. In particular, the size of
the quantum core does not depend on the number of layers and the mass function
is shown to grow linearly with the areal radius up to the outermost layer.
