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arXiv · 0811.0910

The CFT-interpolating Black Hole in Three Dimensions

K. Hotta·Y. Hyakutake·T. Kubota·T. Nishinaka·H. Tanida
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Abstract

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 $\textrm{AdS}_3$ geometries both at the spatial infinity and at the event horizon. An explicit derivation of Virasoro algebras for $\textrm{CFT}_2$ at the two boundaries is shown to be possible à 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 $\textrm{CFT}_2$ living at the infinity and at the horizon. Following the Hamilton-Jacobi analysis by de Boer, Verlinde and Verlinde, we calculate the central charges $c_{\textrm{UV}}$ and $c_{\textrm{IR}}$ for the $\textrm{CFT}_2$ on the infinity and the horizon, respectively. We also confirm that the inequality $c_{\textrm{IR}} < c_{\textrm{UV}}$ is satisfied, which is consistent with the Zamolodchikov's c-theorem.

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K. Hotta, Y. Hyakutake, T. Kubota, T. Nishinaka, H. Tanida. 2008-12-08. The CFT-interpolating Black Hole in Three Dimensions. https://doi.org/10.1088/1126-6708%2F2009%2F01%2F010

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