  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
\`{a} 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.

High Energy Physics - Theory;General Relativity and Quantum Cosmology