Abstract
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.
Highlights
In General Relativity (GR) black holes (BH) are stable geometrical spaces equipped by an event horizon
The thermal AdS solution, obtained by Wick rotating time t = iτ and fixing the periodicity to be τ ≡ τ + β, would generate a dominant contribution to the two-point correlation function at large time interval. This configuration would restore partially information, in [5] it has been shown that the only contribution to the path integral coming from TAdS would not be enough to restore the full information of the pre-BH physics
In this paper we have argued that a two dimensional BH is well described by matching two conformal field theory (CFT) at the ”horizon”
Summary
In General Relativity (GR) black holes (BH) are stable geometrical spaces equipped by an event horizon. The thermal AdS solution, obtained by Wick rotating time t = iτ and fixing the periodicity to be τ ≡ τ + β, would generate a dominant contribution to the two-point correlation function at large time interval This configuration would restore partially information, in [5] it has been shown that the only contribution to the path integral coming from TAdS would not be enough to restore the full information of the pre-BH physics. There, correlations functions must be calculated by considering all the degenerate states This sounds pretty much like the Maldacena (and Hawking) suggestion, where, contrary to the Maldacena case, it has been argued in [8] that those co-existing quantum phases are not exponentially suppressed with respect to the classical BH solution. For us, semiclassical will really mean beyond the one loop approximation of the gravity matter system
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