On Holographic description of the Kerr-Newman-AdS-dS black holes

TL;DR

This paper explores the holographic duality of four-dimensional Kerr-Newman-AdS-dS black holes, revealing hidden conformal symmetry and matching microscopic CFT entropy with macroscopic black hole entropy through scattering and correlator analyses.

Contribution

It demonstrates the existence of hidden conformal symmetry in Kerr-Newman-AdS-dS black holes and establishes their duality to a two-dimensional CFT, extending holographic descriptions to more general black holes.

Findings

Hidden conformal symmetry in near-horizon region

Matching of Bekenstein-Hawking entropy with CFT Cardy formula

Agreement of retarded Green's functions with CFT predictions

Abstract

In this paper, we study the holographic description of the generic four-dimensional non-extremal Kerr-Newman-AdS-dS black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, there exists hidden conformal symmetry on the solution space. Similar to the Kerr case, this suggests that the Kerr-Newman-AdS-dS black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=\frac{6a(r_++r_\ast)}{k}$ and temperatures $T_L=\frac{k(r_+^2+r_\ast^2+2a^2)}{4\pi a\Xi(r_++r_\ast)}, T_R=\frac{k(r_+-r_\ast)}{4\pi a\Xi}$. The macroscopic Bekenstein-Hawking entropy could be recovered from the microscopic counting in dual CFT via the Cardy formula. Using the Minkowski prescription, we compute the real-time correlators of the scalar, photon and graviton in near horizon geometry of near extremal Kerr-AdS-dS black hole. In all these cases, the retarded Green's function and the corresponding absorption cross section are in perfect match with CFT prediction. We further discuss the low-frequency scattering of a charged scalar by a Kerr-Newman-AdS-dS black hole and find the dual CFT description.