We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, nearhorizon AdS2 geometry with constant dilaton and U(1) field and an asymptotic AdS2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge cas of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, cas = 3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, cnh ∝ lQ/√G.
Near-horizon limit of the charged BTZ black hole and AdS(2) quantum gravity
CADONI, MARIANO;
2008
Abstract
We show that the 3D charged Banados-Teitelboim-Zanelli (BTZ) black hole solution interpolates between two different 2D AdS spacetimes: a near-extremal, nearhorizon AdS2 geometry with constant dilaton and U(1) field and an asymptotic AdS2 geometry with a linear dilaton. Thus, the charged BTZ black hole can be considered as interpolating between the two different formulations proposed until now for AdS2 quantum gravity. In both cases the theory is the chiral half of a 2D CFT and describes, respectively, Brown-Hennaux-like boundary deformations and near-horizon excitations. The central charge cas of the asymptotic CFT is determined by 3D Newton constant G and the AdS length l, cas = 3l/G, whereas that of the near-horizon CFT also depends on the U(1) charge Q, cnh ∝ lQ/√G.
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