  Quantum evolution of a scalar field's modes propagating on quantum spacetime
of a collapsing homogeneous dust ball is written effectively, as an evolution
of the same quantum modes on a (semiclassical) dressed geometry. When the
backreaction of the field is discarded, the classical spacetime singularity is
resolved due to quantum gravity effects and is replaced by a quantum bounce on
the dressed collapse background. In the presence of backreaction, the emergent
(interior) dressed geometry becomes mode dependent and the energy density
associated with the backreaction of each mode scales as a radiation fluid.
Semiclassical dynamics of this so-called {\em rainbow} dressed background is
analyzed. It turns out that the backreaction effects speed up the occurrence of
the bounce in comparison to the case where only a dust fluid is present. By
matching the interior and exterior regions at the boundary of dust, a
mode-dependent black hole geometry emerges as the exterior spacetime.
Properties of such a rainbow black hole are discussed. That mode dependence
causes, in particular, a chromatic aberration in the gravitational lensing
process of which maximal magnitude is estimated via calculation of the
so-called Einstein angle.
