Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I - Analytic Results for Quasinormal Modes

TL;DR

This paper analyzes quasinormal modes of extremal charged rotating black holes in AdS_5 x S^5, revealing a spectrum similar to chiral 1+1 CFTs and providing both numerical and some analytic results for decay rates.

Contribution

It introduces a method to compute quasinormal modes of degenerate black holes with zero entropy, connecting gravitational spectra to chiral CFTs and providing new analytic solutions.

Findings

Spectrum resembles that of a chiral 1+1 CFT

Analytic decay rates for scalar perturbations in supersymmetric case

Numerical results obtained for quasinormal modes

Abstract

In this work we discuss charged rotating black holes in $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface operators in a subsector of $\mathcal{N}=4$ SYM. We add a massless uncharged scalar to the five dimensional supergravity theory, such that it still forms a consistent truncation of the type IIB ten dimensional supergravity and analyze its quasinormal modes. Separating the equation of motion to a radial and angular part, we proceed to solve the radial equation using the asymptotic matching expansion method applied to a Heun equation with two nearby singularities. We use the continued fraction method for the angular Heun equation and obtain numerical results for the quasinormal modes. In the case of the supersymmetric black hole we present some analytic results for the decay rates of the scalar perturbations. The spectrum of quasinormal modes obtained is similar to that of a chiral 1+1 CFT, which is consistent with the conjectured field-theoretic dual. In addition, some of the modes can be found analytically.