  We review some features of BEC models of black holes obtained by means of the
HWF formalism. We consider the KG equation for a toy graviton field coupled to
a static matter current in spherical symmetry. The classical field reproduces
the Newtonian potential generated by the matter source, while the corresponding
quantum state is given by a coherent superposition of scalar modes with
continuous occupation number. An attractive self-interaction is needed for
bound states to form, so that (approximately) one mode is allowed, and the
system of N bosons can be self-confined in a volume of the size of the
Schwarzschild radius. The HWF is then used to show that the radius of such a
system corresponds to a proper horizon. The uncertainty in the size of the
horizon is related to the typical energy of Hawking modes: it decreases with
the increasing of the black hole mass (larger number of gravitons), in
agreement with semiclassical calculations and different from a single very
massive particle. The spectrum contains a discrete ground state of energy $m$
(the bosons forming the black hole), and a continuous spectrum with energy
$\omega > m$ (representing the Hawking radiation and modelled with a Planckian
distribution at the expected Hawking temperature). The $N$-particle state can
be collectively described by a single-particle wave-function given by a
superposition of a total ground state with energy $M = N m$ and a Planckian
distribution for $E > M$ at the same Hawking temperature. The partition
function is then found to yield the usual area law for the entropy, with a
logarithmic correction related with the Hawking component. The backreaction of
modes with $\omega > m$ is also shown to reduce the Hawking flux and the
evaporation properly stops for vanishing mass.

General Relativity and Quantum Cosmology;High Energy Physics - Theory;Quantum Physics