Superradiant Instability Research Articles

Phase diagram of the charged black hole bomb system

We find the phase diagram of solutions of the charged black hole bomb system. In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar theory confined in a Minkowski box. We impose boundary conditions such that the scalar field vanishes at and outside a cavity of constant radius. These hairy black holes are asymptotically flat with a scalar condensate floating above the horizon. We identify four critical scalar charges which mark significant changes in the qualitative features of the phase diagram. When they coexist, hairy black holes always have higher entropy than the Reissner-Nordström black hole with the same quasilocal mass and charge. So hairy black holes are natural candidates for the endpoint of the superradiant/near-horizon instabilities of the black hole bomb system. We also relate hairy black holes to the boson stars of the theory. When it has a zero horizon radius limit, the hairy black hole family terminates on the boson star family. Finally, we find the Israel surface tensor of the box required to confine the scalar condensate and that it can obey suitable energy conditions.

Multioscillating black holes

We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within a cohomogeneity-1 ansatz. The onset of the gravitational and scalar field superradiant instabilities of the Myers-Perry-AdS black hole mark bifurcation points to black resonators and hairy Myers-Perry-AdS black holes, respectively. These solutions are subject to the other (gravitational or scalar) instability, and result in hairy black resonators which contain both gravitational and scalar hair. The hairy black resonators have smooth zero-horizon limits that we call graviboson stars. In the hairy black resonator and graviboson solutions, multiple scalar components with different frequencies are excited, and hence these are multioscillating solutions. The phase structure of the solutions are examined in the microcanonical ensemble, i.e. at fixed energy and angular momenta. It is found that the entropy of the hairy black resonator is never the largest among them. We also find that hairy black holes with higher scalar wavenumbers are entropically dominant and occupy more of phase space than those of lower wavenumbers.

Modeling and searching for a stochastic gravitational-wave background from ultralight vector bosons

Ultralight bosons, which are predicted in a variety of beyond-Standard-Model scenarios as dark-matter candidates, can trigger the superradiant instability around spinning black holes. This instability gives rise to oscillating boson condensates which then dissipate through the emission of nearly monochromatic gravitational waves. Such systems are promising sources for current and future gravitational-wave detectors. In this work, we consider minimally-coupled, massive vector bosons, which can produce a significantly stronger gravitational-wave signal compared to the scalar case. We adopt recently obtained numerical results for the gravitational-wave flux, and astrophysical models of black hole populations that include both isolated black holes and binary merger remnants, to compute and study in detail the stochastic gravitational-wave background emitted by these sources. Using a Bayesian framework, we search for such a background signal emitted using data from the first and second observing runs of Advanced LIGO. We find no evidence for such a signal. Therefore, the results allow us to constrain minimally coupled vector fields with masses in the range $0.8\times10^{-13}\mathrm{eV}\leq m_b\leq 6.0\times10^{-13}\mathrm{eV}$ at 95% credibility, assuming optimistically that the dimensionless spin distribution for the isolated black hole population is uniform in the range $[0,1]$. With more pessimistic assumptions, a narrower range around $m_b\approx 10^{-13}\mathrm{eV}$ can still be excluded as long as the upper end of the uniform distribution for dimensionless black hole spin is $\gtrsim 0.2$.

Characterising the most rapidly rotating AdS5-Kerr black holes

Classical censorship permits AdS5-Kerr black holes with arbitrarily large angular momenta per unit mass, which does not seem reasonable from a holographic point of view. However, it has been shown that, when these black holes are embedded in string theory, their angular momentum per unit mass is in fact bounded by , where L is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS5-Kerr black holes, with angular momentum per unit mass close to this bound, might be unstable, for example, to a superradiant instability. We show that this is not always true: there is a small domain in the AdS5-Kerr parameter space corresponding to black holes which are stable against superradiance and yet nearly saturate the stringy bound.

Boson stars and solitons confined in a Minkowski box

We consider the static charged black hole bomb system, originally designed for a (uncharged) rotating superradiant system by Press and Teukolsky. A charged scalar field confined in a Minkowski cavity with a Maxwell gauge field has a quantized spectrum of normal modes that can fit inside the box. Back-reacting non-linearly these normal modes, we find the hairy solitons, a.k.a boson stars (depending on the chosen U(1) gauge), of the theory. The scalar condensate is totally confined inside the box and, outside it, we have the Reissner-Nordström solution. The Israel junction conditions at the box surface layer determine the stress tensor that the box must have to confine the scalar hair. Some of these horizonless hairy solutions exist for any value of the scalar field charge and not only above the natural critical charges of the theory (namely, the critical charges for the onset of the near-horizon and superradiant instabilities of the Reissner-Nordström black hole). However, the ground state solutions have a non-trivial intricate phase diagram with a main and a secondary family of solitons (some with a Chandrasekhar mass limit but others without) and there are a third and a fourth critical scalar field charges where the soliton spectra changes radically. Most of these intricate properties are not captured by a higher order perturbative analysis of the problem where we simply back-react a normal mode of the system.

Black hole superradiance in the presence of Lorentz symmetry violation

In this paper we consider the massive scalar perturbation on the top of a small spinning-like black hole in context of Einstein-bumblebee modified gravity in order to probe the role of spontaneous Lorentz symmetry breaking on the superradiance scattering and corresponding instability. We show that at the low-frequency limit of the scalar wave the superradiance scattering will be enhanced with the Lorentz-violating parameter $\alpha<0$ and will be weakened with $\alpha>0$. Moreover, by addressing the black hole bomb issue, we extract an improved bound in the instability regime indicating that $\alpha<0$ increases the parameter space of the scalar field instability, while $\alpha>0$ decreases it.

Renormalization group analysis of superradiant growth of self-interacting axion cloud

Abstract There are strong interests in considering ultra-light scalar fields (especially axion) around a rapidly rotating black hole because of the possibility of observing gravitational waves from axion condensate (axion cloud) around black holes. Motivated by this consideration, we propose a new method to study the dynamics of an ultra-light scalar field with self-interaction around a rapidly rotating black hole, which uses the dynamical renormalization group method. We find that for relativistic clouds, saturation of the superradiant instability by the scattering of the axion due to the self-interaction does not occur in the weakly non-linear regime when we consider the adiabatic growth of the cloud from a single superradiant mode. This may suggest that for relativistic axion clouds, an explosive phenomenon called the Bosenova may inevitably happen, at least once in its evolutionary history.

About magnetic AdS black holes

There has recently been a strong revival of interest in quasi-extremal magnetically charged black holes. In the asymptotically flat case, it is possible to choose the magnetic charge of such an object in such a manner that the black hole is surrounded by a corona in which electroweak symmetry is restored on macroscopic scales, a result of very considerable interest. We argue that holographic duality indicates that the asymptotically AdS analogues of these black holes have several interesting properties: the dual theory is only physical if the black hole is required to rotate; in the rotating case, the magnetic field at the poles does not attain its maximum on the event horizon, but rather somewhat outside it; the magnetic field at the equator is not a monotonically decreasing function of the magnetic charge; the electric fields induced by the rotation, while smaller than their magnetic counterparts, are by no means negligible; the maximal electric field often occurs neither at the poles nor at the equator; and so on. Most importantly, in the magnetically charged case it is possible to avoid the superradiant instability to which neutral AdS-Kerr black holes are subject; but the need to avoid this instability imposes upper bounds on the magnetic and electric fields. In some circumstances, therefore, the corona may not exist in the asymptotically AdS case.

The tune of the Universe: the role of plasma in tests of strong-field gravity

ABSTRACT Gravitational-wave (GW) astronomy, together with precise pulsar timing and long baseline interferometry, is changing our ability to perform tests of fundamental physics with astrophysical observations. Some of these tests are based on electromagnetic (EM) probes or electrically charged bodies, and assume an empty Universe. However, the cosmos is filled with plasma, a dilute medium which prevents the propagation of low-frequency, small-amplitude EM waves. We show that the plasma hinders our ability to perform some strong-field gravity tests, in particular: (i) nonlinear plasma effects dramatically quench plasma-driven super-radiant instabilities; (ii) the contribution of EM emission to the inspiral of charged black-hole binaries is strongly suppressed; (iii) EM-driven secondary modes, although present in the spectrum of charged black holes, are excited to negligible amplitude in the GW ringdown signal. The last two effects are relevant also in the case of massive fields that propagate in vacuum and can jeopardize tests of modified theories of gravity containing massive degrees of freedom.

Acoustic black-hole bombs and scalar clouds in a photon-fluid model

Massive bosonic fields in the background of a Kerr black hole can either trigger superradiant instabilities (black-hole bombs) or form equilibrium configurations corresponding to pure bound states, known as stationary scalar clouds. Here, similar phenomena are shown to emerge in the fluctuation dynamics of a rotating photon-fluid model. In the presence of suitable vortex flows, the density fluctuations are governed by the massive Klein-Gordon equation on a ($2+1$) curved spacetime, possessing an ergoregion and an event horizon. We report on superradiant instabilities originating from quasibound phonon states trapped by the vortex background and, remarkably, on the existence of stationary modes in synchronous rotation with the horizon. These represent the acoustic counterpart of astrophysical scalar clouds. Our system offers a promising platform for analogue gravity experiments on superradiant instabilities of massive bosons and black-hole-field equilibrium configurations.

A note on the linear stability of black holes in quadratic gravity

Black holes in f(R)-gravity are known to be unstable, especially the rotating ones. In particular, an instability develops that looks like the classical black hole bomb mechanism: the linearized modified Einstein equations are characterized by an effective mass that acts like a massive scalar perturbation on the Kerr solution in general relativity, which is known to yield instabilities. In this note, we consider a special class of f(R) gravity that has the property of being scale-invariant. As a prototype, we consider the simplest case f(R)=R^2 and show that, in opposition to the general case, static and stationary black holes are stable, at least at the linear level. Finally, the result is generalized to a wider class of f(R) theories.

Rotating tensor-multiscalar black holes with two scalars

We construct hairy black hole solutions in a particular set of tensor-multi-scalar theories of gravity for which the target-space admits a Killing vector field with periodic flow that is furthermore the generator of a one-parameter family of point transformations which leave the whole theory invariant. As for black holes with scalar hair in general relativity, these must be rotating objects as the scalarization arises from superradiant instability. We analyze the most fundamental rotating solutions (winding number $m=1$) in five theories which differ from each other by the value of the Gauss curvature of the target-space. The domain of existence of these solutions is investigated, as well as their hairyness, horizon area and deformation factor.

Gravitational wave echoes induced by a point mass plunging into a black hole

Abstract Recently, the possibility of detecting gravitational wave echoes in the data stream subsequent to the binary black hole mergers observed by LIGO was suggested. Motivated by this suggestion, we presented templates of echoes based on black hole perturbations in our previous work. There, we assumed that the incident waves resulting in echoes are similar to the ones that directly escape to the asymptotic infinity. In this work, to extract more reliable information on the waveform of echoes without using the naive assumption on the incident waves, we investigate gravitational waves induced by a point mass plunging into a Kerr black hole. We solve the linear perturbation equation with the source term induced by the plunging mass under the purely outgoing boundary condition at infinity and a hypothetical reflection boundary condition near the horizon. We find that the low-frequency component below the threshold of the super-radiant instability is highly suppressed, which is consistent with the incident waveform assumed in the previous analysis. We also find that the high-frequency mode excitation is significantly larger than the one used in the previous analysis, if we adopt the perfectly reflective boundary condition independently of the frequency. When we use a simple template in which the same waveform as the direct emissions to infinity is repeated with the decreasing amplitude, the correlation between the expected signal and the template turns out to decrease very rapidly.

Final state of instabilities in Born-Infeld black holes

We study two types of linear instabilities in Einstein-Born-Infeld-scalar field theory and show that small Born-Infeld (BI) black holes suffer from superradiant instability within a particular range of frequencies; the larger the BI coupling parameter, the slower the growth rate of the instability. It is predicted that a small BI black hole decays into a small hairy black hole that has a charged scalar condensate floating near the horizon. We numerically show that there is a phase transition between hairy and BI black holes. The metric solution shows the existence of a hairy black hole for T<Tc and a BI black hole for T>Tc. In addition, the BI black hole will suffer from tachyonic mass, resulting in a near horizon scalar condensation instability, which is related to a planar hairy black hole. We show that the BI coupling parameter has a direct relation to the critical temperature in the small hairy black hole framework. This is not true for planar hairy black holes where a larger BI coupling parameter leads to a smaller critical temperature. Finally, it is shown that a small hairy black hole is stable at the critical temperature so it can be considered as the end point of superradiant instability.

Clockwork mechanism to remove superradiance limits

The superradiant instability of black hole space-times has been used to place limits on ultra-light bosonic particles. We show that these limits are model dependent. While the initial growth of the mode is gravitational and thus model independent, the ability to place a limit on new particles requires the mode to grow unhindered to a large number density. Non-linear interactions between the particle and other light degrees of freedom that are mediated through higher dimension operators can damp this growth, eliminating the limit. However, these non-linearities may also destroy a cosmic abundance of these light particles, an attractive avenue for their discovery in several experiments. We study the specific example of the QCD axion and show that it is easy to construct models where these non-linearities eliminate limits from superradiance while preserving their cosmic abundance.

Characterizing the continuous gravitational-wave signal from boson clouds around Galactic isolated black holes

Ultralight bosons can form large clouds around stellar-mass black holes via the superradiance instability. Through processes such as annihilation, these bosons can source continuous gravitational wave signals with frequencies within the range of LIGO and Virgo. If boson annihilation occurs, then the Galactic black hole population will give rise to many gravitational signals; we refer to this as the ensemble signal. We characterize the ensemble signal as observed by the gravitational-wave detectors; this is important because the ensemble signal carries the primary signature that a continuous wave signal has a boson annihilation origin. We explore how a broad set of black hole population parameters affects the resulting spin-0 boson annihilation signal and consider its detectability by recent searches for continuous gravitational waves. A population of $10^8$ black holes with masses up to $30\mathrm{M}_\odot$ and a flat dimensionless initial spin distribution between zero and unity produces up to a thousand signals loud enough to be in principle detected by these searches. For a more moderately spinning population the number of signals drops by about an order of magnitude, still yielding up to a hundred detectable signals for some boson masses. A non-detection of annihilation signals at frequencies between 100 and 1200 Hz disfavors the existence of scalar bosons with rest energies between $2\times10^{-13}$ and $2.5\times10^{-12}$ eV. Finally we show that, depending on the black hole population parameters, care must be taken in assuming that the continuous wave upper limits from searches for isolated signals are still valid for signals that are part of a dense ensemble: Between 200 and 300 Hz, we urge caution when interpreting a null result for bosons between 4 and $6\times10^{-13}$ eV.

Numerical investigation of plasma-driven superradiant instabilities

Photons propagating in a plasma acquire an effective mass μ, which is given by the plasma frequency and which scales with the square root of the plasma density. As noted previously in the literature, for electron number densities ne ∼ 10−3 cm−3 (such as those measured in the interstellar medium) the effective mass induced by the plasma is μ ∼ 10−12 eV. This would cause superradiant instabilities for spinning black holes of a few tens of solar masses. An obvious problem with this picture is that densities in the vicinity of black holes are much higher than in the interstellar medium because of accretion, and possibly also pair production. We have conducted numerical simulations of the superradiant instability in spinning black holes surrounded by a plasma with density increasing closer to the black hole, in order to mimic the effect of accretion. While we confirm that superradiant instabilities appear for plasma densities that are sufficiently low near the black hole, we find that astrophysically realistic accretion disks are unlikely to trigger such instabilities.

Accessing the axion via compact object binaries

Black holes in binaries with other compact objects can provide natural venues for indirect detection of axions or other ultralight fields. The superradiant instability associated with a rapidly spinning black hole leads to the creation of an axion cloud which carries energy and angular momentum from the black hole. This cloud will then decay via gravitational wave emission. We show that the energy lost as a result of this process tends toward an outspiraling of the binary orbit. A given binary system is sensitive to a narrow range of axion masses, determined by the mass of the black hole. This proposal provides a complementary alternative to other approaches for detecting or constraining light particles created by superradiance, such as directly measuring the black hole spin or detecting the resulting gravitational wave signal. Pulsar-black hole binaries, once detected in the electromagnetic band, will allow high-precision measurements of black hole mass loss via timing measurements of the companion pulsar. This avenue of investigation is particularly promising in light of the recent preliminary announcements of two candidate black hole-neutron star mergers by LIGO/Virgo (#S190814bv and #S190426c). We demonstrate that for such a binary system with a typical millisecond pulsar and a 3M⊙ black hole, axions with masses between 2.7 × 10−12 eV and 3.2 × 10−12 eV are detectable. Recent gravitational wave observations by LIGO/Virgo of binary black hole mergers imply that, for these binaries, gravitational radiation from the rotating quadrupole moment is a dominant effect, causing an inspiraling orbit. With some reasonable assumptions about the period of the binary when it formed and the spins of the black holes, these observations rule out possible axion masses between 3 × 10−13 eV and 6 × 10−13 eV . Future binary black hole observations, for example by LISA, are expected to provide more robust bounds. In some circumstances, neutron stars may also undergo superradiant instabilities, and binary pulsars could be used to exclude axions with certain masses and matter couplings.

Superradiance and stability of the regularized 4D charged Einstein-Gauss-Bonnet black hole

We investigated the superradiance and stability of the regularized 4D charged Einstein-Gauss-Bonnet black hole which is recently inspired by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. We found that the positive Gauss-Bonnet coupling constant α enhances the superradiance, while the negative α suppresses it. The condition for superradiant instability is proved. We also worked out the quasinormal modes (QNMs) of the charged Einstein-Gauss-Bonnet black hole and found that the real part of all the QNMs does not satisfy the superradiance condition and the imaginary parts are all negative. Therefore this black hole is stable. When α makes the black hole extremal, there are normal modes.

Superradiant instabilities for a charged black hole in de Rham-Gabadadze-Tolley theory

In this paper, we study the superradiant instabilities for the charged furry black hole in massive gravity. In de Rham-Gabadadze-Tolley (dRGT) theory, the St\uckelberg field may provide St\uckelberg hair for the black hole solutions. To make the furry most obvious in large scale, we only consider to the next order of $1/{r}^{2}$ in the metric function. According to the horizon, we define two new conservation charge as the hair of black hole: one is positive charge ${k}_{+}$; the other is negative charge ${k}_{\ensuremath{-}}$. Both of them are known as St\uckelberg charge. Using a mirrorlike boundary condition, we show that there are superradiant instabilities for both types of black holes. As the St\uckelberg charge increases, the central black hole becomes more stable. The reason for this behavior is caused by the impact of St\uckelberg charge on the horizon. We also plot the parameter space for stabilities of two types black holes. As a matter of fact, the various configuration of St\uckelberg field led to this new feature in the dRGT theory.