  We consider general relativistic homogeneous gravitational collapses for dust
and radiation. We show that replacing the density profile with an effective
density justified by some quantum gravity framework leads to the avoidance of
the final singularity. The effective density acts on the collapsing cloud by
introducing an isotropic pressure, which is negligible at the beginning of the
collapse and becomes negative and dominant in the strong field regime. Event
horizons never form and therefore the outcome of the collapse is not a black
hole, in the sense that there are no regions causally disconnected from future
null infinity. Apparent horizons form when the mass of the object exceeds a
critical value, disappear when the matter density approaches an upper bound and
gravity becomes very weak (asymptotic freedom regime), form again after the
bounce as a consequence of the decrease in the matter density, and eventually
disappear when the density becomes too low and the matter is radiated away. The
possibility of detecting radiation coming from the high density region of a
collapsing astrophysical object in which classically there would be the
creation of a singularity could open a new window to experimentally test
theories of quantum gravity.
