Abstract
Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher dimensions, focusing on slowly rotating charged AdS black holes with a single angular momentum. We divide the spacetime of these black holes into the near-horizon and far regions and find solutions to the scalar wave equation in each of these regions. Next, we perform the matching of these solutions in the overlap between the regions, by employing the idea that the orbital quantum number $ \ell $ can be thought of as an approximate integer. Thus, we obtain the complete low-frequency solution that allows us to calculate the complex frequency spectrum of quasinormal modes, whose imaginary part is determined by a small damping parameter. Finally, we find a remarkably instructive expression for the damping parameter, which appears to be a complex quantity in general. We show that the real part of the damping parameter can be used to give a {\it universal} analytic description of the superradiant instability for slowly rotating charged AdS black holes in all spacetime dimensions.
Highlights
In the spirit of these fruitful ideas, Starobinsky [6] developed a quantitative theory of superradiance for scalar waves in the Kerr metric
It is the nonvanishing mass of a bosonic field that provides a natural mirror around the black hole, thereby resulting in the superradiant instability of bound state modes of the bosonic field
Performing a detailed analysis of this expression for all pertinent cases, as the orbital quantum number approaches a non-negative integer, we have concluded that its real part correctly describes the negative damping of modes in the regime of superradiance, i.e. the superradiant instability of the higher-dimensional anti-de Sitter (AdS) black holes under consideration
Summary
In the spirit of these fruitful ideas, Starobinsky [6] developed a quantitative theory of superradiance for scalar waves in the Kerr metric. It has recently been shown that the instability time scale for these bound state modes may become orders of magnitude shorter in many cases of physical interest [14,15,16,17,18,19] and giving rise to potentially observable effects of the superradiant instability. In this regard, the case of ultralight axions appearing in the “axiverse” scenario [20] of string theory compactifications is intriguing. It appears that for axions in a certain mass range, the time scale of the superradiant instability becomes significantly short, creating gaps in the mass–spin spectrum of astrophysical black holes [20]
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