Gravitational quasinormal modes of AdS black branes in d spacetime dimensions

TL;DR

This paper analyzes the complete gravitational quasinormal mode spectra of AdS black branes in arbitrary dimensions, elucidating boundary conditions and confirming hydrodynamic behavior through analytical and numerical methods.

Contribution

It provides a comprehensive study of quasinormal modes in d-dimensional AdS black branes, including boundary conditions and dispersion relations, extending previous work to arbitrary dimensions.

Findings

Confirmed hydrodynamic behavior of low-frequency modes

Derived dispersion relations for various regimes

Validated results with analytical and numerical methods

Abstract

The AdS/CFT duality has established a mapping between quantities in the bulk AdS black-hole physics and observables in a boundary finite-temperature field theory. Such a relationship appears to be valid for an arbitrary number of spacetime dimensions, extrapolating the original formulations of Maldacena's correspondence. In the same sense properties like the hydrodynamic behavior of AdS black-hole fluctuations have been proved to be universal. We investigate in this work the complete quasinormal spectra of gravitational perturbations of $d$-dimensional plane-symmetric AdS black holes (black branes). Holographically the frequencies of the quasinormal modes correspond to the poles of two-point correlation functions of the field-theory stress-energy tensor. The important issue of the correct boundary condition to be imposed on the gauge-invariant perturbation fields at the AdS boundary is studied and elucidated in a fully $d$-dimensional context. We obtain the dispersion relations of the first few modes in the low-, intermediate- and high-wavenumber regimes. The sound-wave (shear-mode) behavior of scalar (vector)-type low-frequency quasinormal mode is analytically and numerically confirmed. These results are found employing both a power series method and a direct numerical integration scheme.