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Register a new userSuperradiant instability of black resonators and geons
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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.
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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 $Rtimes SU(2)$. 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 $Omega>1$ 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.
Rapidly rotating Myers-Perry-AdS$_5$ (MPAdS$_5$) black holes are shown to be unstable against rotational superradiance of a Maxwell field. From the onset of the instability, time-periodic neutral black hole solutions equipped with a nontrivial electromagnetic wave are obtained, which we call {it photonic black resonators}. In the horizonless limit, they reduce to geon solutions which may be called {it photon stars}. Specifically, we introduce a cohomogeneity-1 ansatz for the metric and Maxwell field and construct such solutions with an $Rtimes SU(2)$ isometry group. We compute thermodynamic quantities and obtain phase diagrams. It turns out that a photonic black resonator has a higher entropy than a MPAdS$_5$ black hole, while it also has a smaller entropy than a black resonator without the Maxwell field. This suggests what is expected for nonlinear dynamics following the Maxwell superradiant instability with the $SU(2)$ isometry.
We consider the evolution of black hole involving an $f(R)$ global monopole based on the Extended Uncertainty Principle (EUP). The black hole evolutions refer to the instability due to the Parikh-Kraus-Wilczeck tunneling radiation or fragmentation. It is found that the EUP corrections make the entropy difference larger to encourage the black hole to radiate more greatly. We also show that the appearance of the EUP effects result in the black holes division. The influence from global monopole and the revision of general relativity can also adjust the black hole evolution simultaneously, but can not change the final result that the black hole will not be stable because of the EUPs effects.
We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct hairy black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.
I present evidence of a novel guise of superradiance that arises in black hole binary spacetimes. Given the right initial conditions, a wave will be amplified as it scatters off the binary. This process, which extracts energy from the orbital motion, is driven by absorption across the horizons and is most pronounced when the individual black holes are not spinning. Focusing on real scalar fields, I demonstrate how modern effective field theory (EFT) techniques enable the computation of the superradiant amplification factor analytically when there exist large separations of scales. Although exploiting these hierarchies inevitably means that the amplification factor is always negligible (it is never larger than about one part in $10^{10}$) in the EFTs regime of validity, this work has interesting theoretical implications for our understanding of general relativity and lays the groundwork for future studies on superradiant phenomena in binary systems.
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