  It is logically possible that regularly evaporating black holes exist in
nature. In fact, the prevalent theoretical view is that these are indeed the
real objects behind the curtain in astrophysical scenarios. There are several
proposals for regularizing the classical singularity of black holes so that
their formation and evaporation do not lead to information-loss problems. One
characteristic is shared by most of these proposals: these regularly
evaporating black holes present long-lived trapping horizons, with absolutely
enormous evaporation lifetimes in whatever measure. Guided by the discomfort
with these enormous and thus inaccessible lifetimes, we elaborate here on an
alternative regularization of the classical singularity, previously proposed by
the authors in an emergent gravity framework, which leads to a completely
different scenario. In our scheme the collapse of a stellar object would result
in a genuine time-symmetric bounce, which in geometrical terms amounts to the
connection of a black-hole geometry with a white-hole geometry in a regular
manner. The two most differential characteristics of this proposal are: i) the
complete bouncing geometry is a solution of standard classical general
relativity everywhere except in a transient region that necessarily extends
beyond the gravitational radius associated with the total mass of the
collapsing object; and ii) the duration of the bounce as seen by external
observers is very brief (fractions of milliseconds for neutron-star-like
collapses). This scenario motivates the search for new forms of stellar
equilibrium different from black holes. In a brief epilogue we compare our
proposal with a similar geometrical setting recently proposed by Haggard and
Rovelli.
