Superradiant instability of black resonators and geons

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.

Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids

“…For the compatible operators, L 2 , L z , and W 3 , their simultaneous eigenfunctions are the Wigner-D functions, D J KM (θ, φ, ψ) [81][82][83]. We have the following eigenvalue equations:…”

Resonating AdS soliton

“…Therefore, it will be prone to further superradiant instabilities [44]. Stability analysis has been carried out for five-dimensional cohomogeneity-1 solutions [45], and cascades of instabilities are expected, but their endpoint is an open problem [43]. A study of such of nonlinear evolution is [46].…”

“…On the one hand, it would be interesting to look at linear perturbations of the resonating AdS soliton. In global AdS space, cohomogeneity-1 geons are linearly stable in a large portion of parameter space [45], and the current horizonless solution may share the same property, especially in the branch of small deformation, while the highly deformed branch may have a different behavior and show linear instability instead.…”

Multioscillating black holes

“…the metric functions depend only on a single variable, and the solution can be obtained by solving ODEs) were constructed in [23]. The scalar, electromagnetic, and gravitational quasinormal modes of these black resonators were studied shortly thereafter in [24]. 1 As anticipated, black resonators are unstable to higher modes.…”

“…Then in section 3, we describe details of our ansatz. Sections 4 and 5 review the Myers-Perry-AdS solution, geons, and black resonators in this ansatz, which were studied in [23,24]. Section 6 discusses hairy black holes and boson stars which are higher multiplet versions of those in [9].…”