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

TL;DR

This paper calculates low-lying gravitational quasinormal modes in a four-dimensional AdS-Schwarzschild black hole, revealing their connection to boundary hydrodynamics and proposing a Robin boundary condition for the master field.

Contribution

It introduces a Robin boundary condition for the master field in gravitational perturbations, leading to the discovery of low-lying modes that align with hydrodynamic predictions.

Findings

Low-lying modes match linearized hydrodynamics predictions.

A family of modes with frequencies following an arithmetic progression.

Robin boundary condition is favored over Dirichlet for the master field.

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.