Abstract
Black resonators and geons in global AdS are rapidly rotating, low-energy solutions with a helical Killing field. We study the linear mode stability of equal angular momenta, five-dimensional black resonators and geons under scalar, electromagnetic, and gravitational perturbations. We find that black resonators are unstable to the superradiant instability, in agreement with previously known results. Perhaps surprisingly, many geons appear linearly stable, despite having an ergoregion. This apparent stability implies that geons are important long-lived, low-energy states in the dual gauge theory. However, we do find that geons are unstable within a certain range of parameter space. We comment on the nature of this instability and to its possible endpoints. We also report on new non-spinning oscillating geons, which we construct within a cohomogeneity two ansatz. Given the existing arguments that suggest our linear stability results may be extended nonlinearly, our findings indicate that most geons are generic and long-lived solutions.
Highlights
In recent years, there has been an increased focus on gravitational dynamics in anti-de Sitter space (AdS), due in large part to the development of gauge/gravity duality [1,2,3]
We show the location of the onsets for the superradiant instability on black resonators for three modes with j = 9/2, j = 5, and j = 11/2
MPAdS at branching points of black resonators are stable for j ≤ 4, as we explain in section A.3 of the appendix
Summary
There has been an increased focus on gravitational dynamics in anti-de Sitter space (AdS), due in large part to the development of gauge/gravity duality [1,2,3]. Generic configurations contain angular momentum, which implies that the black hole will be rapidly rotating Such a black hole is superradiant [21,22,23] (see [24] for a review) and can amplify waves that approach its horizon. Our understanding of low-energy states in AdS hinges upon the endpoint of the superradiant instability of rapidly rotating black holes and the stability of geons, both of which remain open problems. Black resonators form intermediate states in the dynamics of superradiant instabilities [35, 36] The nature of these instabilities, say in Kerr-AdS, is such that one unstable mode often dominates the dynamics at early times.
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