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We revisit the peculiar electromagnetic quasinormal mode spectrum of anasymptotically anti-de Sitter Schwarzschild black hole. Recent numericalcalculations have shown that some quasinormal mode frequencies become purelyoverdamped at some critical black hole sizes, where the spectrum alsobifurcates. In this paper, we shed light on unnoticed and unexplainedproperties of this spectrum by exploiting some novel analytic results for thelarge black hole limit. We demonstrate, both numerically and analytically, thatthe quasinormal mode spectra of large black holes become approximatelyisospectral, and refer to this new symmetry property as spectral similarity. Wetake advantage of this spectral similarity to derive a precise analyticexpression for the locations of the bifurcations, in which a surprisingFeigenbaum-like constant appears. We derive an exact solution for its spectrumand eigenfunctions, and find that large black holes cannot be made to vibratewith electromagnetic perturbations, independently of the boundary conditionsimposed at spatial infinity. Finally, we characterize the insensitivity of thespectrum to different boundary conditions by analyzing the expansion of thequasinormal mode spectrum around the large black hole limit.

physical review. d/physical review. d.

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