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Germani, Cristiano (2014): On the many saddle points description of quantum black holes. In: Physics Letters B, Vol. 733: pp. 93-99




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. (C) 2014 The Author