On quasinormal modes of small Schwarzschild-Anti-de-Sitter black hole

TL;DR

This paper analyzes the decay modes of scalar fields around small Schwarzschild-Anti-de-Sitter black holes, revealing how their quasinormal frequencies behave as the black hole size diminishes, aligning with previous theoretical predictions.

Contribution

It provides detailed calculations of quasinormal modes for small Schwarzschild-AdS black holes, extending understanding of their spectral properties in the small horizon limit.

Findings

Imaginary part of frequency approaches zero as $r_+^{d-2}$

Real part of frequency decreases to a minimum then approaches $d-1$

Modes tend to AdS modes as $r_+ -> 0$

Abstract

We compute the quasinormal modes associated with decay of the massless scalar filed around a small Schwarzschild-Anti-de-Sitter black hole. The computations shows that when the horizon radius is much less than the anti-de-Sitter radius, the imaginary part of the frequency goes to zero as $r_+^{d-2}$ while the real part of $\omega$ decreases to its minimum and then goes to $d-1$. Thus the quasinormal modes approach the usual AdS modes in the limit $r_+ -> 0$. This agrees with suggestions of Horowitz et al (Phys.Rev. D62 024027 (2000)).