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

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 ${c_L} = {c_R} = \frac{{6a\left( {{r_{+} } + {r_*}} \right)}}{k}$ and temperatures ${T_L} = \frac{{k\left( {r_{+}^2 + r_*^2 + 2{a^2}} \right)}}{{4\pi a \Xi \left( {{r_{+} } + {r_*}} \right)}}$, ${T_R} = \frac{{k\left( {{r_{+} } - {r_*}} \right)}}{{4\pi a\Xi }}$. 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 functions and the corresponding absorption cross sections 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.