  In this work we continue our previous studies concerning the possibility of
the existence of a Bose-Einstein condensate in the interior of a static black
hole, a possibility first advocated by Dvali and G\'omez. We find that the
phenomenon seems to be rather generic and it is associated to the presence of
an horizon, acting as a confining potential. We extend the previous
considerations to a Reissner-Nordstr\"om black hole and to the de Sitter
cosmological horizon. In the latter case the use of static coordinates is
essential to understand the physical picture. In order to see whether a BEC is
preferred, we use the Brown-York quasilocal energy, finding that a condensate
is energetically favourable in all cases in the classically forbidden region.
The Brown-York quasilocal energy also allows us to derive a quasilocal
potential, whose consequences we explore. Assuming the validity of this
quasilocal potential allows us to suggest a possible mechanism to generate a
graviton condensate in black holes. However, this mechanism appears not to be
feasible in order to generate a quantum condensate behind the cosmological de
Sitter horizon.
