Gravitational quasinormal modes for Anti-de Sitter black holes

TL;DR

This work analyzes gravitational quasinormal modes of four-dimensional black holes in both de Sitter and anti-de Sitter spacetimes. It employs Leaver's continued-fraction technique to compute axial (and via duality, polar) perturbation spectra, showing that de Sitter modes admit accurate analytic estimates via a Poschl-Teller potential and yielding a clear large-l asymptotic form. In AdS, boundary conditions are constrained by ADS-CFT; preserving axial-polar duality leads to a one-parameter Robin-type family with axial Dirichlet conditions, producing a spectrum that is only weakly sensitive to the boundary parameter. The results illuminate how holographic boundary conditions influence gravitational quasinormal modes and point toward connections with thermal widths in the boundary CFT and extensions to higher-dimensional cases where perturbation separation is more challenging.

Abstract

Quasinormal mode spectra for gravitational perturbations of black holes in four dimensional de Sitter and anti-de Sitter space are investigated. The anti-de Sitter case is relevant to the ADS-CFT correspondence in superstring theory. The ADS-CFT correspondence suggests a prefered set of boundary conditions.

Figures (6)

• Figure 1: Real (left) and imaginary (right) parts of the gravitational quasinormal mode frequencies $r_1\omega$ with $l=2$ plotted as a function of the surface gravity $r_1\kappa_1$, together with the Pöschl-Teller approximation.
• Figure 2: Real (left) and imaginary (right) parts of the gravitational quasinormal mode frequencies $r_1\omega$ with $l=3$ plotted as a function of the surface gravity $r_1\kappa_1$, together with the Pöschl-Teller approximation.
• Figure 3: The frequencies of the first few quasinormal modes for the black hole anti-de Sitter metric with dirichlet axial boundary conditions and $a\kappa_1=2.0$ (and $r_1=a$). Results for $l=2$, $3$ and $10$ are shown.
• Figure 4: The dependence of the first two quasinormal mode frequencies on the metric parameters for $l=2$ is shown for the dirichlet axial boundary conditions. The frequency with $\omega_R=0$ is also plotted and designated 'special'.
• Figure 5: The frequencies of the first few quasinormal modes for the black hole anti-de Sitter metric with the dirichlet polar boundary conditions ($\gamma=0$) and $\kappa_1a=2.0$ (and $r_1=a$). Results for $l=2$, $3$ and $10$ are shown.