  A star that collapses gravitationally can reach a further stage of its life,
where quantum-gravitational pressure counteracts weight. The duration of this
stage is very short in the star proper time, yielding a bounce, but extremely
long seen from the outside, because of the huge gravitational time dilation.
Since the onset of quantum-gravitational effects is governed by energy density
---not by size--- the star can be much larger than planckian in this phase. The
object emerging at the end of the Hawking evaporation of a black hole can then
be larger than planckian by a factor $(m/m_{\scriptscriptstyle P})^n$, where
$m$ is the mass fallen into the hole, $m_{\scriptscriptstyle P}$ is the Planck
mass, and $n$ is positive. We consider arguments for $n=1/3$ and for $n=1$.
There is no causality violation or faster-than-light propagation. The existence
of these objects alleviates the black-hole information paradox. More
interestingly, these objects could have astrophysical and cosmological
interest: they produce a detectable signal, of quantum gravitational origin,
around the $10^{-14} cm$ wavelength.
