Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes

TL;DR

This paper demonstrates that Breit-Wigner resonances can be effectively used to compute quasinormal modes of anti-de Sitter black holes, especially small ones, with results aligning well with analytical predictions and relevant for AdS/CFT studies.

Contribution

It introduces the resonance method as an efficient numerical tool for calculating black hole quasinormal modes in AdS spacetime, particularly for small black holes.

Findings

Resonance method outperforms traditional series expansion for small SAdS black holes.

Damping timescale scales as r_+^(-2l-2), matching analytic results.

Long-lived modes exist in the eikonal limit, confirming previous predictions.

Abstract

The purpose of this short communication is to show that the theory of Breit-Wigner resonances can be used as an efficient numerical tool to compute black hole quasinormal modes. For illustration we focus on the Schwarzschild anti-de Sitter (SAdS) spacetime. The resonance method is better suited to small SAdS black holes than the traditional series expansion method, allowing us to confirm that the damping timescale of small SAdS black holes for scalar and gravitational fields is proportional to r_+^(-2l-2), where r_+ is the horizon radius. The proportionality coefficients are in good agreement with analytic calculations. We also examine the eikonal limit of SAdS quasinormal modes, confirming quantitatively Festuccia and Liu's prediction of the existence of very long-lived modes in asymptotically AdS spacetimes. Our results are particularly relevant for the AdS/CFT correspondence, since long-lived modes presumably dominate the decay timescale of the perturbations.