Low-lying gravitational modes in the scalar sector of the global AdS_4 black hole

TL;DR

The authors study scalar gravitational perturbations of the global AdS_4–Schwarzschild black hole using the Kodama–Ishibashi master-field formalism and argue that a Robin boundary condition is the physically appropriate choice to avoid deformations of the boundary metric. They perform a numerical analysis to extract quasinormal modes (QNMs) and find a family of low-lying modes that agree with linearized hydrodynamics on the boundary S^2×R, in addition to a tower of higher-frequency modes with approximate arithmetic progression. The work clarifies how boundary conditions connect bulk QNMs to boundary field theory dynamics via AdS/CFT and demonstrates a direct holographic interpretation of the low-lying scalar modes as hydrodynamic excitations. Overall, it highlights the crucial role of boundary conditions in matching gravitational perturbations to boundary fluid behavior in AdS_4.

Abstract

We compute the quasinormal frequencies corresponding to the scalar sector of gravitational perturbations in the four-dimensional AdS-Schwarzschild black hole by using the master field formalism of hep-th/0305147. We argue that the non-deformation of the boundary metric favors a Robin boundary condition on the master field over the usual Dirichlet boundary condition mostly used in the literature. Using this Robin boundary condition we find a family of low-lying modes, whose frequencies match closely with predictions from linearized hydrodynamics on the boundary. In addition to the low-lying modes, we also see the usual sequence of modes with frequencies almost following an arithmetic progression.

Figures (1)

• Figure 1: The zeroes of $s(y)$ represented as crosses in the complex plane. The red cross at $y=0$ denotes a simple zero, while the green crosses denote double zeroes. We use a series expansion in region (i), numerical integration in region (ii), and another series expansion in region (iii).