# Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

## TL;DR

This paper analyzes the quasinormal modes of Gauss-Bonnet-AdS black holes, revealing two distinct mode types and discussing stability conditions, with implications for holographic duality and viscosity bounds.

## Contribution

It provides a detailed characterization of the quasinormal spectrum of Gauss-Bonnet-AdS black holes, including perturbative and non-perturbative modes, and explores stability regimes relevant for holography.

## Key findings

- Two types of quasinormal modes identified: perturbative and non-perturbative.
- Perturbative modes can be approximated by linear corrections to Schwarzschild-AdS modes.
- Black holes become unstable when the Gauss-Bonnet coupling exceeds certain bounds.

## Abstract

Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling $\alpha$. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in $\alpha$ correction to the damping rates: $\omega \approx Re(\omega_{SAdS}) - Im(\omega_{SAdS}) (1 - \alpha \cdot ((D+1) (D-4) /2 R^2)) i$, where $R$ is the AdS radius. The non-perturbative branch of modes consists of purely imaginary modes, whose damping rates unboundedly increase when $\alpha$ goes to zero. When the black hole radius is much larger than the anti-de Sitter radius $R$, the regime of the black hole with planar horizon (black brane) is reproduced. If the Gauss-Bonnet coupling $\alpha$ (or used in holography $\lambda_{GB}$) is not small enough, then the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity. For example, $D=5$ black brane is unstable at $|\lambda_{GB}|>1/8$ and has anomalously large relaxation time when approaching the threshold of instability.