  Considering two dimensional gravity coupled to a CFT, we show that a
semiclassical black hole can be described in terms of two Liouville theories
matched at the horizon. The black hole exterior corresponds to a space-like
while the interior to a time-like Liouville theory. This matching automatically
implies that a semiclassical black hole has an infinite entropy. The path
integral description of the time-like Liouville theory (the Black Hole
interior) is studied and it is found that the correlation functions of the
coupled CFT-gravity system are dominated by two (complex) saddle points, even
in the semiclassical limit. We argue that this system can be interpreted as two
interacting Bose-Einstein condensates constructed out of two degenerate quantum
states. In AdS/CFT context, the same system is mapped into two interacting
strings intersecting inside a three-dimensional BTZ black hole. Finally, we
discuss why, beyond the semiclassical approximation, we expect no firewalls
appearing in our system.
