Electromagnetic quasinormal modes of Schwarzschild-anti-de Sitter black holes: Bifurcations, spectral similarity, and exact solutions in the large black hole limit

TL;DR

This paper analyzes electromagnetic quasinormal modes of large Schwarzschild-anti-de Sitter black holes, revealing spectral symmetries, bifurcation points, and exact solutions, enhancing understanding of black hole perturbation spectra in the large size limit.

Contribution

It provides novel analytic results for the large black hole limit, including spectral similarity, precise bifurcation locations, and exact solutions for modes and eigenfunctions.

Findings

Large black holes exhibit approximate isospectrality in their electromagnetic quasinormal modes.

Bifurcation points follow a Feigenbaum-like constant, indicating a universal pattern.

Large black holes cannot be excited to vibrate electromagnetically, regardless of boundary conditions.

Abstract

We revisit the peculiar electromagnetic quasinormal mode spectrum of an asymptotically anti-de Sitter Schwarzschild black hole. Recent numerical calculations have shown that some quasinormal mode frequencies become purely overdamped at some critical black hole sizes, where the spectrum also bifurcates. In this paper, we shed light on unnoticed and unexplained properties of this spectrum by exploiting some novel analytic results for the large black hole limit. We demonstrate, both numerically and analytically, that the quasinormal mode spectra of large black holes become approximately isospectral, and refer to this new symmetry property as spectral similarity. We take advantage of this spectral similarity to derive a precise analytic expression for the locations of the bifurcations, in which a surprising Feigenbaum-like constant appears. We derive an exact solution for its spectrum and eigenfunctions, and find that large black holes cannot be made to vibrate with electromagnetic perturbations, independently of the boundary conditions imposed at spatial infinity. Finally, we characterize the insensitivity of the spectrum to different boundary conditions by analyzing the expansion of the quasinormal mode spectrum around the large black hole limit.