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Register a new userThe CFT-interpolating Black Hole in Three Dimensions
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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 Henneauxs 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 Zamolodchikovs c-theorem.
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We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent z as exact solutions. At the point z=3, exact black hole solutions which are asymptotically Lifshitz arise. These spacetimes are three-dimensional analogues of those that were recently proposed as gravity duals for scale invariant fixed points.
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In three dimensions, there exist modifications of Einsteins gravity akin to the topologically massive gravity that describe massive gravitons about maximally symmetric backgrounds. These theories are built on the three-dimensional version of the Bach tensor (a curl of the Cotton-York tensor) and its higher derivative generalizations; and they are on-shell consistent without a Lagrangian description based on the metric tensor alone. We give a generic construction of these models, find the spectra and compute the conserved quantities for the Banados-Teitelboim-Zanelli black hole.
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