Quasinormal modes of black holes in anti-de Sitter space: a numerical study of the eikonal limit

TL;DR

This study numerically investigates the quasinormal modes of large black holes and branes in anti-de Sitter space, focusing on the eikonal limit relevant for AdS/CFT, revealing qualitative agreement with prior predictions and dimensional corrections.

Contribution

It provides a detailed numerical analysis of gravitational and scalar quasinormal modes in the eikonal limit, including quantitative corrections and dependencies on black hole parameters.

Findings

Confirmation of qualitative features of long-lived modes

Identification of dimensional-dependent correction factors

Analysis of frequency dependence on horizon radius and angular momentum

Abstract

Using series solutions and time-domain evolutions, we probe the eikonal limit of the gravitational and scalar-field quasinormal modes of large black holes and black branes in anti-de Sitter backgrounds. These results are particularly relevant for the AdS/CFT correspondence, since the eikonal regime is characterized by the existence of long-lived modes which (presumably) dominate the decay timescale of the perturbations. We confirm all the main qualitative features of these slowly-damped modes as predicted by Festuccia and Liu (arXiv:0811.1033) for the scalar-field (tensor-type gravitational) fluctuations. However, quantitatively we find dimensional-dependent correction factors. We also investigate the dependence of the QNM frequencies on the horizon radius of the black hole (brane) and the angular momentum (wavenumber) of vector- and scalar-type gravitational perturbations.