Conformal invariance and near-extreme rotating AdS black holes

Abstract

We obtain retarded Green's functions for massless scalar fields in the background of near-extreme, nearhorizon rotating charged black holes of five-dimensional minimal gauged supergravity. The radial part of the (separable) massless Klein-Gordon equation in such general black hole backgrounds is Heun's equation, due to the singularity structure associated with the three black hole horizons. On the other hand, we find the scaling limit for the near-extreme, near-horizon background where the radial equation reduces to a hypergeometric equation whose SL(2,R) 2 symmetry signifies the underlying two-dimensional conformal invariance, with the two sectors governed by the respective Frolov-Thorne temperatures. We obtain retarded Green's functions for massless scalar fields in the background of near-extreme, near-horizon rotating charged black holes of five-dimensional minimal gauged supergravity. The radial part of the (separable) massless Klein-Gordon equation in such general black hole backgrounds is Heun's equation, due to the singularity structure associated with the three black hole horizons. On the other hand, we find the scaling limit for the near-extreme, near-horizon background where the radial equation reduces to a hypergeometric equation whose SLð2; RÞ 2 symmetry signifies the underlying two-dimensional conformal invariance, with the two sectors governed by the respective Frolov-Thorne temperatures.

Wave equation for the Wu black hole

“…The remarkable structure of separability seen in these works has also been found in some gauged supergravity solutions [19][20][21][22][23][24][25][26]. The symmetries of various black hole solutions in supergravity was studied in [27].…”

Addentum to: Conformal invariance and near-extreme rotating AdS black holes

“…The black hole is specified by the mass, two angular momenta, three equal charges and a cosmological constant, parameterized by m, a, b, q and g. 1 We showed that the wave equation was separable, and obtained the general polar angle equation. As for the radial part, we obtained the explicit equation only for zero eigenvalues (m 1 = m 2 = 0) of the azimuthal angle coordinates φ and ψ in the scalar field Ansatz…”

“…Here, κ k 's are the surface gravities (7)(8)(9) and Ω ak and Ω bk are the two angular velocities (10,11) [1,2]. Probing for a single regular singularity makes it possible to determine the structure due to the associated angular velocities, once one has the surface gravities.…”

“…In [1], we studied the massless Klein-Gordon equation for the general non-extreme rotating black hole in minimal five-dimensional gauged supergravity, given by Chong et al in [2]. The black hole is specified by the mass, two angular momenta, three equal charges and a cosmological constant, parameterized by m, a, b, q and g. 1 We showed that the wave equation was separable, and obtained the general polar angle equation.…”

“…G ≡ g 2 is related to the cosmological constant Λ = −6G, c 0 is the separation constant and n k are the 1 The reader should refer to [1] for the explicit form of the metric and its parametrization.…”