Ultralight bosonic fields are compelling dark-matter candidates and arise in a variety of beyond-Standard-Model scenarios. These fields can tap energy and angular momentum from spinning black holes through superradiant instabilities, during which a macroscopic bosonic condensate develops around the black hole. Striking features of this phenomenon include gaps in the spin-mass distribution of astrophysical black holes and a continuous gravitational-wave~(GW) signal emitted by the condensate. So far these processes have been studied in great detail for scalar fields and, more recently, for vector fields. Here we take an important step forward in the black-hole superradiance program by computing, analytically, the instability time scale, the direct GW emission, and the stochastic background, in the case of massive tensor (i.e., spin-$2$) fields. Our analysis is valid for any black hole spin and for small boson masses. The instability of massive spin-$2$ fields shares some properties with the scalar and vector cases, but its phenomenology is much richer, for example there exist multiple modes with comparable instability time scales, and the dominant GW signal is hexadecapolar rather than quadrupolar. Electromagnetic and GW observations of spinning black holes in the mass range $M\in(1,10^{10})M_\odot$ can constrain the mass of a putative spin-$2$ field in the range $10^{-22} \lesssim m_b\,{\rm c^2/eV} \lesssim 10^{-10}$. For $10^{-17}\lesssim m_b\,{\rm c^2/eV}\lesssim 10^{-15}$, the space mission LISA could detect the continuous GW signal for sources at redshift $z=20$, or even larger.
Ultralight bosons can affect the dynamics of spinning black holes (BHs) via superradiant instability, which can lead to a time evolution of the supermassive BH shadow. We study prospects for witnessing the superradiance-induced BH shadow evolution, considering ultralight vector and tensor fields. We introduce two observables sensitive to the shadow time-evolution: the shadow drift, and the variation in the azimuthal angle lapse associated to the photon ring autocorrelation. The two observables are shown to be highly complementary, depending on the observer's inclination angle. Focusing on the …
Ultralight bosons, as important candidates of dark matter, can condense around spinning black holes (BHs) to form long-lived ``boson clouds'' due to superradiance instability. The boson-BH system can be observed through gravitational wave detection and may become a new window to find traces of ultralight bosons. In this letter we explore the effects on the superradiant instability of BHs from the near-horizon microstructure. By introducing the reflection parameter near a BH horizon, we derived analytical results on the corrections to both energy levels of bosonic cloud and its characteristic f…
Ultralight bosonic fields in the mass range $\sim (10^{-20}-10^{-11})\,{\rm eV}$ can trigger a superradiant instability that extracts energy and angular momentum from an astrophysical black hole with mass $M\sim(5,10^{10})M_\odot$, forming a nonspherical, rotating condensate around it. So far, most studies of the evolution and end-state of the instability have been limited to initial data containing only the fastest growing superradiant mode. By studying the evolution of multimode data in a quasi-adiabatic approximation, we show that the dynamics is much richer and depend strongly on the energ…
Direct detection of gravitational waves from several compact binary coalescences has ushered in a new era of astronomy. It has opened up the possibility of detecting ultralight bosons, predicted by extensions of the Standard Model, from their gravitational signatures. This is of particular interest as some of these hypothetical particles could be components of dark matter that are expected to interact very weakly with Standard Model particles, if at all, but they would gravitate as usual. Ultralight bosons can trigger superradiant instabilities of rotating black holes and form bosonic clouds t…
Ultralight bosons are promising dark matter candidates and can trigger superradiant instabilities of spinning black holes (BHs), resulting in long-lived rotating "bosonic clouds" around the BHs and dissipating their energy through the emission of monochromatic gravitational waves (GWs). We focus on the scalar bosons minimally coupled with both isolated stellar-origin BHs (SBH) and their binary merger remnants, and perform Bayesian data analysis to search for the stochastic GW background from all the unstable modes that can trigger the superradiant instabilities using the data of Advanced LIGO …
Self-stimulated avalanche in superradiant axion clouds
Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences (UCAS)（中国科学院大学物理科学学院）；Ningbo University（宁波大学）；International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（中国科学院大学亚太理论物理中心）
Spinning Kerr black holes are known to be superradiantly unstable to massive scalar perturbations. We here prove that the instability regime of the composed Kerr-black-hole-massive-scalar-field system is bounded from above by the dimensionless inequality $Mμ< m \cdot \sqrt{{{2(1+γ) (1-\sqrt{1-γ^2}) - γ^2} \over {4γ^2}}}$, where $\{μ,m\}$ are respectively the proper mass and azimuthal harmonic index of the scalar field and $γ\equiv r_-/r_+$ is the dimensionless ratio between the horizon radii of the black hole. It is further shown that this {\it analytically} derived upper bound on the superrad…
We consider the intermediate and end state behavior of the superradiantly perturbed Kerr black hole. Superradiant scattering in an asymptotically flat background is considered first. The case of a Kerr black hole in an Anti de-Sitter background is then discussed. Specifically we review what is known about the superradiant instability arising in AdS and its possible end state behavior.
In electrovacuum stationary, asymptotically flat black holes in scalar-tensor theories of gravity are described by the Kerr-Newman family of solutions, just as in general relativity. We show that there exist two mechanisms which can render Kerr black holes unstable when matter is present in the vicinity of the black hole, as this induces an effective mass for the scalar. The first mechanism is a tachyonic instability that appears when the effective mass squared is negative, triggering the development of scalar hair --- a black hole version of "spontaneous scalarization". The second instability…
Motivated by possible existence of string axions with ultralight masses, we study gravitational radiation from an axion cloud around a rotating black hole (BH). The axion cloud extracts the rotation energy of the BH by superradiant instability, while it loses energy through the emission of gravitational waves (GWs). In this paper, GWs are treated as perturbations on a fixed background spacetime to derive the energy emission rate. We give an analytic approximate formula for the case where axion's Compton wavelength is much larger than the BH radius, and then, present numerical results without a…
We find two conditions for superradiant instability of Kerr-Newman black holes under a charged massive scalar perturbation by analyzing asymptotic scalar potential and far-region wave function. Actually, they correspond to the condition for getting a trapping well. Also, we obtain the conditions for superradiant stability of Kerr-Newman black holes which states that there is no trapping well. The analysis is applied to Kerr black holes to find a condition for superradiant instability.
We study the superradiant instability of a massive boson around a spinning black hole in full general relativity without assuming spatial symmetries. We focus on the case of a rapidly spinning black hole in the presence of a vector boson with a Compton wavelength comparable to the black hole radius, which is the regime where relativistic effects are maximized. We follow the growth of the boson cloud through superradiance into the nonlinear regime as it spins down the black hole, reaches a maximum energy, and begins to dissipate through the emission of gravitational waves. We find that the supe…
We investigate the superradiant instability of dyonic Reissner-Nordström (dRN) black holes with two charges under a charged massive scalar perturbation. Two conditions for possessing a trapping well are obtained from analyzing asymptotic scalar potential and far-region wave functions. It is clear that the superradiant instability is not allowed in the dRN black holes because the conditions for a trapping well are not compatible with the superradiance condition.
Gravitational atoms produced from the superradiant extraction of rotational energy of spinning black holes can reach energy densities significantly higher than that of dark matter, turning black holes into powerful potential detectors for ultralight bosons. These structures are formed by coherently oscillating bosons, which induce oscillating metric perturbations deflecting photon geodesics passing through their interior. The deviation of nearby geodesics can be further amplified near critical bound photon orbits. We discuss the prospect of detecting this deflection using photon ring autocorre…
We study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca equations. We concentrate on a rapidly spinning black hole ($a=0.99$) and the dominant $m=1$ azimuthal mode of the Proca field, with real and imaginary components of the field chosen to yield an axisymmetric stress-energy tensor and, hence, spacetime. We find that in excess of $9\%$ of the black hole's mass can be transferred into the field. In all cases studied, …
We present an analytical study of superradiant instability of rotating asymptotically Gödel black hole (Kerr-Gödel black hole) in five-dimensional minimal supergravity theory. By employing the matched asymptotic expansion method to solve Klein-Gordon equation of scalar field perturbation, we show that the complex parts of quasinormal frequencies are positive in the regime of superradiance. This implies the growing instability of superradiant modes. The reason for this kind of instability is the Dirichlet boundary condition at asymptotic infinity, which is similar to that of rotating black hole…
We examine the stability of extremal braneworld Reissner-Nordström black holes under massive charged scalar perturbations. We show that similar to the four-dimensional case, the superradiant amplification can occur in braneworld charged holes. More interestingly we find that when the spacetime dimension is higher than four, a trapping potential well can emerge outside the braneworld black hole. This potential well is the extra dimensional effect and does not exist in four dimensions. It triggers the superradiant instability of the extremal braneworld charged holes.
Superradiant instabilities can trigger the formation of bosonic clouds around rotating black holes. If the bosonic field growth is sufficiently fast, these clouds could form shortly after a binary black hole merger. Such clouds are continuous sources of gravitational waves whose detection (or lack thereof) can probe the existence of ultralight bosons (such as axion-like particles) and their properties. Motivated by the binary black hole mergers seen by Advanced LIGO so far, we investigate in detail the parameter space that can be probed with continuous gravitational wave signals from ultraligh…
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordstrom-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass un…
We study the superradiant instability of massive vector fields, i.e. Proca fields, around spinning black holes in the test field limit. This is motivated by the possibility that observations of astrophysical black holes can probe the existence of ultralight bosons subject to this mechanism. By making use of time-domain simulations, we characterize the growth rate, frequency, spatial distribution, and other properties of the unstable modes, including in the regime where the black hole is rapidly spinning and the Compton wavelength of the Proca field is comparable to the black hole radius. We fi…
We study the superradiant instability of slowly rotating Kerr-Newman (sKN) black holes under a charged massive scalar perturbation. These black holes resemble closer the Reissner-Nordström black holes than the Kerr-Newman black holes. We compute the negative absorption cross section of a massive scalar for superradiant scattering in the low frequency limit. From the scalar potential analysis, we find that the superradiant instability is not allowed in the sKN black holes because the condition for a trapping well is not compatible with the superradiance condition. However, the rate of energy ex…
We study the phenomena of superradiance for $F(R)$-Maxwell black holes in an AdS space-time. The AdS boundary plays the role of a mirror and provides a natural confining system that makes the superradiant waves bouncing back and forth between the region near the horizon and the reflective boundary, causing a possible superradiant instability. We obtain numerical solutions for static hairy black holes in this scenario and investigate their instability and explicitly address the stability of such solutions for spherical perturbations under specific conditions for the scalar charge and AdS radius…
We numerically study the superradiant instability of charged massless scalar field in the background of charged stringy black hole with mirror-like boundary condition. We compare the numerical result with the previous analytical result and show the dependencies of this instability upon various parameters of black hole charge $Q$, scalar field charge $q$, and mirror radius $r_m$. Especially, we have observed that imaginary part of BQN frequencies grows with the scalar field charge $q$ rapidly.
Magnetic fields surrounding spinning black holes can confine radiation and trigger superradiant instabilities. To investigate this effect, we perform the first fully-consistent linear analysis of the Ernst spacetime, an exact solution of the Einstein--Maxwell equations describing a black hole immersed in a uniform magnetic field $B$. In the limit in which the black-hole mass vanishes, the background reduces to the marginally stable Melvin spacetime. The presence of an event horizon introduces a small dissipative term, resulting in a set of long-lived -- or unstable -- modes. We provide a simpl…
An exact Kerr-like solution has been obtained recently in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken. In this paper, we investigate the superradiant instability of the Kerr-like black hole under the perturbation of a massive scalar field. We find the Lorentz breaking parameter $L$ does not affect the superradiance regime or the regime of the bound states. However, since $L$ appears in the metric and its effect cannot be erased by redefining the rotation parameter $\tilde{a}=\sqrt{1+L}a$, it indeed affects the bound state spectrum and the superradiance. We c…
When a scalar wave perturbation is properly scattering off a charged or rotating black hole, the energy of the reflected scalar wave may be amplified. This is a superradiant process. If this amplification process can occur back and forth through certain confining mechanism, it will lead to strong instability of the black hole. In this paper, the superradiant stability is investigated for a special kind of dyonic black holes in string theory. Although the dynoic black hole has a similar spacetime metric with a electrically charged RN black hole, it is found that the dyonic black hole is more un…
The superradiant instability of Kerr-AdS black holes is studied by numerically solving the full 3+1 dimensional Einstein equations. We find that the superradiant instability results in a two stage process with distinct initial and secondary instabilities. At the end of the secondary instability the geometry oscillates at several distinct fundamental frequencies -- a multi-oscillating black hole. The multi-oscillating black hole is remarkably close to a black resonator, albeit with a bit of gravitational hair. During the hairy black resonator epoch, the evolution of the horizon area is consiste…
Ultralight scalar fields around spinning black holes can trigger superradiant instabilities, forming a long-lived bosonic condensate outside the horizon. We use numerical solutions of the perturbed field equations and astrophysical models of massive and stellar-mass black hole populations to compute, for the first time, the stochastic gravitational-wave background from these sources. In optimistic scenarios the background is observable by Advanced LIGO and LISA for field masses $m_s$ in the range $\sim [2\times 10^{-13}, 10^{-12}]\,{\rm eV}$ and $\sim 5\times[ 10^{-19}, 10^{-16}]\,{\rm eV}$, r…
We investigate in detail the mechanism of superradiance to render the instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant. We also discuss the spontaneous scalarization in the de Sitter background and find that this instability can also happen in the spherical de Sitter configuration in a special style.
We investigate the superradiant instability of Kerr black holes under a massive scalar perturbation. We obtain a potential $V_i(r)$ when expanding the scalar potential $V_K(r)$ for large $r$. The Newton potential $V_1(r)$ and the far-region potential $V_2(r)$ are used to explore the superradiant instability, while $V_3(r)$ matches a geodesic potential $V_{gK}(r)$ for a neutral particle moving around the Kerr black hole. Thus, $V_{gK}(r)$ is employed to fix the separation constant. We obtain a condition for a trapping well to possess a quasibound state in the Kerr black holes by analyzing the N…
We investigate the superradiant (in)stability of the extremal multi-charge static black holes in the STU supergravity model, which reduce to the RN black hole when all the charges are equal. We first show that the frequency of quasi-bound states is necessarily complex and obtain the corresponding superradiant condition. We then study the effective potential of the Schrödinger-like equation associated with the radial function of the charged scalar field. We find that trapping-well configurations can emerge with either a single peak or double peaks. We numerically obtain the corresponding unstab…
In this work, we obtain quasibound states of a massive scalar around the Kerr black hole. A massive scalar propagating around the Kerr black hole induces the far-region potential with either a trapping well or a tiny well, which produces a peak of resonance or a bound state in the far-region. The former represents superradiant instability, while the latter could accommodate superradiant instability via a positive $ω_I$. If the scalar's energy is really quantized around a tiny well, an ultralight boson could be expressed in terms of a hydrogen-like bound state, leading to a gravitational atom w…
We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein's equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the transverse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instabili…
We study the superradiance instability of charged massive scalar field in the background of Kerr-Newman-anti-de Sitter black hole. By employing the asymptotic matching technique to solve Klein-Gordon equation analytically, the complex parts of quasinormal frequencies are shown to be positive in the regime of superradiance. Because the calculation is performed in the approximation of small black hole, the result indicates that small Kerr-Newman-anti-de Sitter black hole is unstable against the massive scalar field perturbation with small charge.
One class of competitive candidates for dark matter is ultralight bosons. If they exist, these bosons may form long-lived bosonic clouds surrounding rotating black holes via superradiant instabilities, acting as sources of gravity and affecting the propagation of gravitational waves around the host black hole. During extreme-mass-ratio inspirals, the bosonic clouds will survive the inspiral phase and can affect the quasinormal-mode frequencies of the perturbed black-hole-bosonic-cloud system. In this work, we compute the shifts of gravitational quasinormal-mode frequencies of a rotating black …
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 theor…
Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such process, however, is only efficient if resonant: when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field-black hole equilibrium state - a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87…
Superradiant instabilities of spinning black holes can be used to impose strong constraints on ultralight bosons, thus turning black holes into effective particle detectors. However, very little is known about the development of the instability and whether its nonlinear time evolution accords to the linear intuition. For the first time, we attack this problem by studying the impact of gravitational-wave emission and gas accretion on the evolution of the instability. Our quasi-adiabatic, fully-relativistic analysis shows that: (i) gravitational-wave emission does not have a significant effect o…
It has long been known that dissipation is a crucial ingredient in the superradiant amplification of wavepackets off rotating objects. We show that, once appropriate dissipation mechanisms are included, stars are also prone to superradiance and superradiant instabilities. In particular, ultra-light dark matter with small interaction cross section with the star material or self-annihilation can trigger a superradiant instability. On long timescales, the instability strips the star of most of its angular momentum. Whether or not new stationary configurations surrounded by scalar condensates exis…
We study the instability of near extremal and extremal four-dimensional AdS charged hairy black hole to radial neutral massive and charged massless scalar field perturbations. We solve the scalar field equation by using the improved asymptotic iteration method and the time domain analysis and we find the quasinormal frequencies. For the charged scalar perturbations, we find the superradiance condition by computing the reflection coefficient in the low-frequency limit and we show that in the superradiance regime, which depends on the scalar hair charge, all modes of radial charged massless pert…
It has been shown that the mass of the scalar field in the charged stringy black hole is never able to generate a potential well outside the event horizon to trap the superradiant modes. This is to say that the charged stringy black hole is stable against the massive charged scalar perturbation. In this paper we will study the superradiant instability of the massless scalar field in the background of charged stringy black hole due to a mirror-like boundary condition. The analytical expression of the unstable superradiant modes is derived by using the asymptotic matching method. It is also poin…
In this paper, a detailed analysis for superradiant stability of the system composed by a $D$-dimensional Reissner-Nordström-anti-de Sitter (RN-AdS) black hole and a reflecting mirror under charged scalar perturbations are presented in the linear regime. It is found that the stability of the system is heavily affected by the mirror radius as well as the mass of the scalar perturbation, AdS radius and the dimension of space-time. In a higher dimensional space-time, the degree of instability of the superradiant modes will be severely weakened. Nevertheless, the degree of instability can be magni…
In the presence of an ultralight bosonic field, spinning black holes are unstable to superradiance. The rotational energy of the black hole is converted into a non-axisymmetric, oscillating boson cloud which dissipates through the emission of nearly monochromatic gravitational radiation. Thus, gravitational wave observations by ground- or space-based detectors can be used to probe the existence of dark particles weakly coupled to the Standard Model. In this work, we focus on massive vector bosons, which grow much faster through superradiance, and produce significantly stronger gravitational wa…
We point out that 5D large radius doubly spinning black rings with rotation along S^1 and S^2 are afflicted by a robust instability. It is triggered by superradiant bound state modes. The Kaluza-Klein momentum of the mode along the ring is responsible for the bound state. This kind of instability in black strings and branes was first suggested by Marolf and Palmer and studied in detail by Cardoso, Lemos and Yoshida. We find the frequency spectrum and timescale of this instability in the black ring background, and show that it is active for large radius rings with large rotation along S^2. We i…
We study the propagation of charged scalar fields in the background of $2+1$-dimensional Coulomb-like AdS black holes, and we show that such propagation is unstable under Dirichlet boundary conditions. However, all the unstable modes are superradiant and all the stable modes are non-superradiant, according with the superradiant condition. Mainly, we show that when the scalar field is charged the quasinormal frecuencies (QNFs) are always complex, contrary to the uncharged case, where for small values of the black hole charge the complex QNFs are dominant, while that for bigger values of the bla…
We consider the bound states of the massive scalar field around a rotating black hole immersed in the asymptotically uniform magnetic field. In the regime of slow black hole rotation, the Klein-Gordon equation allows separation of variables. We show that the growth rate of the instability can be amplified a few times by the magnetic field. The effect occurs because the magnetic field adds the "effective mass" term $B |m|$ to the scalar field potential for a Kerr black hole. In addition, and as a by-product, we discuss the behavior of the quasinormal modes for the magnetized rotating black hole…
