Chaos and pole-skipping in rotating black holes

Abstract

We study the connection between many-body quantum chaos and energy dynamics for the holographic theory dual to the Kerr-AdS black hole. In particular, we determine a partial differential equation governing the angular profile of gravitational shock waves that are relevant for the computation of out-of-time ordered correlation functions (OTOCs). Further we show that this shock wave profile is directly related to the behaviour of energy fluctuations in the boundary theory. In particular, we demonstrate using the Teukolsky formalism that at complex frequency ω * = i2πT there exists an extra ingoing solution to the linearised Einstein equations whenever the angular profile of metric perturbations near the horizon satisfies this shock wave equation. As a result, for metric perturbations with such temporal and angular profiles we find that the energy density response of the boundary theory exhibit the signatures of "pole-skipping" -namely, it is undefined, but exhibits a collective mode upon a parametrically small deformation of the profile. Additionally, we provide an explicit computation of the OTOC in the equatorial plane for slowly rotating large black holes, and show that its form can be used to obtain constraints on the dispersion relations of collective modes in the dual CFT. Contents 1 Introduction 1 2 The Kerr-AdS Black Hole 4 3 OTOCs in Kerr-AdS black holes 7 3.1 Equatorial OTOC in Kerr-AdS black holes 10 4 Near-horizon metric perturbations of Kerr-AdS 13 5 Pole-skipping and quasinormal modes in Kerr-AdS 15 5.1 The Teukolsky equations 16 5.2 Existence of extra ingoing modes 18 5.3 Quasinormal modes and pole-skipping 23 5.4 Equatorial OTOC and pole-skipping in the slowly rotating limit 25 6 Discussion 28 A Kerr-AdS metric in Kruskal-like coordinates 31 B Shock wave profile in slowly-rotating limit 32 C Additional details of Teukolsky formalism 33 D Explicit demonstration of existence of a quasinormal mode 35

Irregular Liouville correlators and connection formulae for Heun functions

“…In our viewpoint this intriguing correspondence could be further clarified in CFT terms, as started in [13], and other massive gravitational sources can be studied along the same lines by making use of the results of this paper. For related topics, see also [53,54,55,56,57,58].…”

Irregular Liouville Correlators and Connection Formulae for Heun Functions

“…In our viewpoint this intriguing correspondence could be further clarified in CFT terms, as started in [13], and other massive gravitational sources can be studied along the same lines by making use of the results of this paper. For related topics, see also [53][54][55][56][57][58]. • Our analysis can be extended to irregular blocks on Riemann surfaces of higher genus.…”