  In a previous paper, we studied the interior solution of a collapsing body in
a non-local theory of gravity super-renormalizable at the quantum level. We
found that the classical singularity is replaced by a bounce, after which the
body starts expanding. A black hole, strictly speaking, never forms. The
gravitational collapse does not create an event horizon but only an apparent
one for a finite time. In this paper, we solve the equations of motion assuming
that the exterior solution is static. With such an assumption, we are able to
reconstruct the solution in the whole spacetime, namely in both the exterior
and interior regions. Now the gravitational collapse creates an event horizon
in a finite comoving time, but the central singularity is approached in an
infinite time. We argue that these black holes should be unstable, providing a
link between the scenarios with and without black holes. Indeed, we find a non
catastrophic ghost-instability of the metric in the exterior region.
Interestingly, under certain conditions, the lifetime of our black holes
exactly scales as the Hawking evaporation time.
