Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter spacetimes: A complete study on the asymptotic behavior

TL;DR

This paper thoroughly analyzes the asymptotic behavior of quasinormal modes of Schwarzschild-AdS black holes across different sizes, revealing universal high overtone spacing and isospectrality between scalar and gravitational perturbations.

Contribution

It extends previous work by computing higher overtones for all black hole regimes and proves the universality and isospectrality of high overtone modes.

Findings

High overtones are evenly spaced across all black hole sizes.

Mode spacing is universal and independent of the field type.

Scalar and gravitational perturbations are asymptotically isospectral.

Abstract

We present a thorough analysis for the quasinormal (QN) behavior, associated with the decay of scalar, electromagnetic and gravitational perturbations, of Schwarzschild-anti-de Sitter black holes. As it is known the anti-de Sitter (AdS) QN spectrum crucially depends on the relative size of the black hole to the AdS radius. There are three different types of behavior depending on whether the black hole is large, intermediate, or small. The results of previous works, concerning lower overtones for large black holes, are completed here by obtaining higher overtones for all the three black hole regimes. There are two major conclusions that one can draw from this work: First, asymptotically for high overtones, all the modes are evenly spaced, and this holds for all three types of regime, large, intermediate and small black holes, independently of l, where l is the quantum number characterizing the angular distribution; Second, the spacing between modes is apparently universal, in that it does not depend on the field, i.e., scalar, electromagnetic and gravitational QN modes all have the same spacing for high overtones. We are also able to prove why scalar and gravitational perturbations are isospectral, asymptotically for high overtones, by introducing appropriate superpartner potentials.