An analysis of the wave equation for the U (1) ² gauged supergravity black hole

Abstract

Abstract. We study the massless Klein-Gordon equation in the background of the most general rotating dyonic AdS black hole in gauged N = 2, U (1) 2 gauged supergravity in D = 4, given by Chow and Compère [Phys. Rev. D89 (2014) 065003]. The angular part of the separable wave equation is of the Heun type, while the radial part is a Fuchsian equation with five regular singularities. The radial equation is further analyzed and written in a specific form, that reveals the pole structure of the horizon equation, whose residua are expressed in terms of the surface gravities and angular velocities associated with respective horizons. The near-horizon (near-)extremal limits of the solution are also studied, where the expected hidden conformal symmetry is revealed. Furthermore, we present the retarded Green's functions for these limiting cases. We also comment on the generality of the charge-dependent parts of the metric parameters and address some further examples of limiting cases.

STU black holes and SgrA⋆

“…We should note that classes of rotating black holes in gauged supergravity theories also admit a separation for both the null and timelike geodesics, which is again a consequence of the separability of the minimally-coupled massless scalar equations in these backgrounds, c.f., [55]. Thus the extension of the analysis presented in this paper to supergravity black holes with non-zero cosmological constant would provide interesting examples for studying the effects of the cosmological constant in the calculation of the properties of black hole shadows.…”

Specific form of the wave equation for nonextremal black holes

“…For the most general four dimensional gauged solution in N = 2, U (1) 2 supergravity given by Chow and Compère in Ref. 5, the radial part was shown to have this structure 6 . Also, for the most general black hole solution of five-dimensional maximally supersymmetric gauged supergravity with U (1) 3 gauge symmetry given in Ref.…”

Strong cosmic censorship in near-extremal Kerr-Sen-de Sitter spacetime

“…In the Boyer-Lindquist coordinates, the KSdS black hole solutions deriving from the above equations of motion read [46][47][48]…”

“…In this paper, we will investigate the SCC for the Kerr-Sen black hole [45] with a positive cosmological constant, i.e., the Kerr-Sen-de Sitter (KSdS) black hole [46][47][48]. Compared with the Kerr-Newman-de Sitter black hole, the KSdS black hole has distinct characteristics.…”