Remarks on holographic models of the Kerr-AdS5 geometry

Abstract

We study the low-temperature limit of scalar perturbations of the Kerr-AdS5 black-hole for generic rotational parameters. We motivate the study by considering real-time holography of small black hole backgrounds. Using the isomonodromic technique, we show that corrections to the extremal limit can be encoded in the monodromy parameters of the Painlevé V transcendent, whose expansion is given in terms of irregular chiral conformal blocks. After discussing the contribution of the intermediate states to the quasinormal modes, we perform a numerical analysis of the low-lying frequencies. We find that the fundamental mode is perturbatively stable at low temperatures for small black holes and that excited perturbations are superradiant, as expected from thermodynamical considerations. We close by considering the holographic interpretation of the unstable modes and the decaying process.

Absorption cross section in gravity’s rainbow from confluent Heun equation

“…We study the case ℓ = 0 because the leading behavior of a 0 − 1/2 is of the order ω2 , which suggests a scaling limit between ã0 , ã1 , and Λ. Hence, one has to sum the ω2 contributions from all the orders in Λ, as shown in [24][25][26]. Namely, a ℓ (ℓ = 0) ≡ a 0 reads…”

“…Typically, the resulting ODEs possess a finite number of regular (irregular) singular points depending on the background and the presence of horizons, e.g. the dynamics of massless scalar fields in Kerr-(anti)-de Sitter black holes will reduce to two Heun equations [19], where the connection between the Heun accessory parameter and the four-point Virasoro conformal blocks [20] brought a new application for the computation of quasi-normal modes (QNMs) [21][22][23][24][25][26] in terms of an isomonodromic tau function formulated in [27]. The latter step was made under the Alday-Gaiotto-Tachikawa (AGT) correspondence, where the semi-classical limit of the Liouville CFT corresponds to the Nekrasov-Shatashvili (NS) limit of a 4D N = 2 SU(2) supersymmetric gauge theory [28].…”

Holographic thermal correlators from supersymmetric instantons

“…[28]. 4 See also [43][44][45] for a different approach based on Painlevé equations. and numerically.…”

More on the SW-QNM correspondence

“…Quite recently, attempting exact WKB quantization techniques [20][21][22][23][24][25], a new astonishing gauge-gravity connection between the QNM spectral problem and quantum Seiberg-Witten (SW) curves [26][27][28] for N = 2 SYM theories was suggested and tested in the case of Kerr BHs in 4-d [29]. It is worth mentioning that similar problems have been studied using the monodromy properties of differential equations yielding similar results [30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”