Chaos and pole-skipping in rotating black holes

TL;DR

This work establishes a concrete link between quantum chaos, as diagnosed by out-of-time-ordered correlators (OTOCs), and energy-density dynamics in the holographic Kerr-AdS/CFT setting. By deriving a horizon shock-wave equation and employing the Teukolsky formalism, it shows that pole-skipping—an intrinsic non-uniqueness in ingoing gravitational perturbations—occurs when the near-horizon angular profile satisfies the shock-wave equation, and that this is tied to the OTOC's chaotic growth. In the slowly rotating, large-black-hole regime, the authors obtain an explicit equatorial OTOC and relate its angular structure to the dispersion of boundary collective modes through pole-skipping points, providing constraints on QNM spectra. Overall, the paper extends the chaos–hydrodynamics correspondence to rotating holographic systems and offers a framework to probe how rotation modifies chaotic and hydrodynamic observables in strongly coupled CFTs.

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 $ω_* = i 2 πT$ 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.