Calculating quasinormal modes of Schwarzschild anti-de Sitter black holes using the continued fraction method

TL;DR

This paper computes quasinormal modes of Schwarzschild anti-de Sitter black holes using the continued fraction method, confirming some previous results and revealing new insights into mode convergence and bifurcation phenomena.

Contribution

It applies the continued fraction method to compute quasinormal modes, connecting numerical results with analytic formulas and clarifying the behavior of high overtone modes.

Findings

Low overtone modes agree with previous results.

High overtone modes rapidly approach asymptotic formulas.

No high overtone modes with high frequency and low damping found.

Abstract

We investigate the scalar, gravitational, and electromagnetic quasinormal mode spectra of Schwarzschild anti-de Sitter black holes using the numerical continued fraction method. The spectra have similar, almost linear structures. With a few exceptions, the low overtone quasinormal modes are consistent with previously obtained results in the literature that use other numerical techniques. The intermediate and high overtone quasinormal modes, in comparison to the Schwarzschild case, converge very quickly to the asymptotic formulas previously obtained by analytic monodromy techniques. In addition, we find a connection between the analytic asymptotic formulas and the purely imaginary modes. In particular, these formulas can be used to predict the bifurcation of the lowest damped electromagnetic modes. Finally, we find no high overtone quasinormal modes with high oscillation frequency and low damping, which had been previously predicted.