Black resonators and geons in AdS ₅

Abstract

We construct dynamical black hole solutions with a helical symmetry in AdS 5 , called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric describing a class of black resonators and geons whose isometry group is R × SU(2). This allows us to study them in a wide range of parameters. We obtain the phase diagram for the black resonators, geons, and Myers-Perry-AdS 5 , where the black resonators emerge from the onset of a superradiant instability of the Myers-Perry-AdS 5 with equal angular momenta and are connected to the geons in the small horizon limit. The angular velocities of the black resonators always satisfy Ω > 1 in units of the AdS radius. A black resonator is shown to have higher entropy than a Myers-Perry-AdS 5 black hole with the same asymptotic charges. This implies that the Myers-Perry-AdS 5 can dynamically evolve into the black resonator under the exact SU(2)-symmetry although its endpoint will be further unstable to SU(2)-violating perturbations.

Superradiant instability of black resonators and geons

“…This lack of symmetry poses a challenge in studying the stability of these solutions. But recently, by going to five dimensions and exploiting the extra symmetries that emerge when both angular momenta are equal, the authors in [43] have constructed black resonators and geons where the metric is cohomogeneity-1 (i.e. the metric functions have a single variable).…”

Photonic black resonators and photon stars in AdS5

“…In comparison, in the geons studied in Ref. [21], we did not find such turning points as long as we constructed solutions within numerical limitations. In the photon star solutions we constructed, the angular velocity always satisfies Ω > 1 although it decreases from the value Ω = 2 of the pure AdS.…”

Resonating AdS soliton

“…But recently, by going to five dimensions, geons whose metric is cohomogeneity-1 (i.e. the metric functions only depend on a single variable) have been constructed [27,28]. By applying techniques in refs.…”

“…By applying techniques in refs. [27,28], we construct the resonating AdS soliton with cohomogeneity-1 metric in five dimensions. There has been a perturbative construction [29], but we are able to find non-trivial nonlinear solutions.…”

“…The normal modes of the AdS space are connected to the onset of the superradiant instability of rotating black holes [20,[33][34][35][36][37][38][39][40][41]. Indeed, gravitational geons correspond to the smooth horizonless limit of black resonators [27,28,42,43]. 3 A black resonator is a dynamical spacetime.…”