The CFT-interpolating black hole in three dimensions

We present a new exact black hole solution in three dimensional Einstein gravity coupled to a single scalar field. This is one of the extended solutions of the BTZ black hole and has in fact AdS(3) geometries both at the spatial infinity and at the event horizon. An explicit derivation of Virasoro algebras for CFT2 at the two boundaries is shown to be possible h la Brown and Henneaux's calculation. If we regard the scalar field as a running coupling in the dual two dimensional field theory, and its flow in the bulk as the holographic renormalization group flow, our black hole should interpolate the two CFT2 living at the infinity and at the horizon. Following the Hamilton-Jacobi analysis by de Boer, Verlinde and Verlinde, we calculate the central charges c(UV) and C-IR for the CFT2 on the infinity and the horizon, respectively. We also confirm that the inequality C-IR < C-UV is satisfied, which is consistent with the Zamolodchikov's c-theorem.