AdS 2 /CFT 1 correspondence and near-extremal black hole entropy

Abstract

We provide a realization of the AdS 2 /CFT 1 correspondence in terms of asymptotic symmetries of the AdS 2 ×S 1 and AdS 2 ×S 2 geometries arising in near-extremal BTZ and Reissner-Nordström black holes. Cardy's formula exactly accounts for the deviation of the Bekenstein-Hawking entropy from extremality. We also argue that this result can be extended to more general black holes near extremality. * jnavarro@lie.uv.es † pnavarro@lie.uv.es

Three dimensional origin of AdS 2 quantum gravity

“…After the DLCQ limiting procedure the solution (4.5) reads 12) and the coordinate identifications (4.6) simplify to (3.10), now in the form The metric (4.12) is superficially similar to (4.5) but it differs in two crucial aspects. First, as we have emphasized, the scaling (4.9) unwraps the compact coordinate w − in (4.5) so that it becomes non-compact in (4.12).…”

THE AdS/CFT CORRESPONDENCE IN TWO DIMENSIONS

“…The value C = 24Φ 0 was found, which turned out to be wrong by a factor of 2 [2,7] (see also Ref. [9]). The puzzle was resolved independently in Refs [10], [11].…”

Holography, degenerate horizons and entropy

“…Imposing spherical symmetry on the metric 19) where l 2 = G (4) , x µ are the 2D coordinates (t, x) and dΩ 2 is the metric on the twosphere, and assuming a radial electric field 20) the above action reduces to 21) and redefining 23) we arrive at…”

“…In Sect.3 we shall show, also in a parallel way, that the deviation of the Bekenstein-Hawking entropy of nearly degenerate black holes from the entropy of the degenerate solution can be derived, via Cardy's formula [25], from the Virasoro algebra of asymptotic symmetries. We shall emphasize the fact that this mechanism, already introduced in [19], works for both situations: for asymptotic geometries of the form AdS 2 ×S 2 and also dS 2 ×S 2 . In Sect.4 we shall generalize the above results for Reissner-Nordström and Schwarzschild-de Sitter black holes in any dimension.…”

“…This type of realization of the AdS/CFT correspondence [15,16] was analyzed for the Jackiw-Teitelboim mode of 2D gravity in [17,18] and further studied in [19] in connection with gravity theories around extremal black hole solutions. The extremal BTZ and four-dimensional Reissner-Nordström black holes possess geometries of the form AdS 2 ×S 1 and AdS 2 ×S 2 respectively.…”