Superradiant Instability Research Articles

Superradiant energy extraction from rotating hairy Horndeski black holes

Adopting the manifestation of low frequency and low mass for the scalar perturbation, we perform a semiclassical analysis of the superradiance phenomenon for a rotating hairy Horndeski black hole (BH). For the spacetime under study enriched by the hairy Horndeski parameter $h$, in addition to the mass $M$ and spin $a$, we compute the amplification factor of scalar wave scattering indicating the energy extraction from the BH. We find that due to the addition of the hairy parameter $h$ in the geometry, the superradiance scattering and its frequency range enhance compared to the Kerr BH. This implies that Horndeski's gravity belongs to those alternative theories of gravity that make the amplification factor larger than the Kerr BH so that the energy extraction in its framework is more efficient than general relativity. Calculating the outgoing energy flux measured by an observer at infinity verifies the role of the hairy parameter $h$ in the increase in energy extraction efficiency from the rotating BH. By implementing the BH bomb mechanism, we present an analysis of the superradiant instability of the underlying BH spacetime against massive scalar fields. Our analysis indicates that the hairy Horndeski parameter leaves no imprint on the standard superradiant instability regime.

Superradiance of massive scalar particles around rotating regular black holes* *Supported in part by the National Natural Science Foundation of China (11675081, 12175108)

Regular black holes, as part of an important attempt to eliminate the singularities in general relativity, have been of wide concern. Because the superradiance associated with rotating regular black holes plays an indispensable role in black hole physics, we calculate the superradiance related effects, i.e., the superradiance instability and the energy extraction efficiency, for a scalar particle with a small mass around a rotating regular black hole, where the rotating regular black hole is constructed by the modified Newman-Janis algorithm. We analytically give the eigenfrequency associated with instability and the amplification factor associated with energy extraction. For two specific models, i.e., the rotating Hayward and Bardeen black holes, we investigate how their regularization parameters affect the growth of instability and the efficiency of energy extraction from the two rotating regular black holes. We find that the regularization parameters give rise to different modes of the superradiance instability and the energy extraction when the rotation parameters vary. There are two modes for the growth of superradiance instability and four modes for the energy extraction. Our results show the diversity of superradiance in the competition between the regularization parameter and the rotation parameter for rotating regular black holes.

Subdominant modes of the scalar superradiant instability and gravitational wave beats

Ultralight scalars could extract energy and angular momentum from a Kerr black hole (BH) because of superradiant instability. Multiple modes labelled with $nlm$ grow while rotating around the BH, emitting continuous gravitational wave (GW). In this work, we carefully study the contribution of the subdominant modes with $n\geq 1$ in the evolution of the BH-condensate system. We find the BH still evolves along the Regge trajectory of the $n=0$ modes even with the presence of the subdominant modes. The interference of the dominant and the subdominant modes produces beats in the emitted GW, which could be used to distinguish the BH-condensate systems from other monochromatic GW sources, such as neutron stars.

Black hole superradiance in dynamical Chern-Simons gravity

Black hole superradiance provides a window into the dynamics of light scalar fields and their interactions close to a rotating black hole. Due to the rotation of the black hole, the amplitude of the scalar field becomes magnified, leading to a "black hole bomb" effect. Recent work has demonstrated that rotating black holes in dynamical Chern-Simons gravity possess unique structures, the "Chern-Simons caps," which may influence the behavior of matter near the black hole. Motivated by the presence of these caps, we study superradiance in dynamical Chern-Simons gravity in the context of a slowly rotating black hole. We find that additional modes are excited and contribute to the superradiance beyond what is expected for a Kerr black hole. Studying the superradiant spectrum of perturbations, we find that the Chern-Simons contributions give rise to small corrections to the angular dependence of the resulting scalar cloud. Finally, we comment on potential observable consequences and future avenues for investigation.

Superradiant axion clouds around asteroid-mass primordial black holes

We analyze the dynamics and observational signatures of axion clouds formed via the superradiant instability around primordial black holes, focusing on the mass range 1014 - 1018 kg where the latter may account for all the dark matter.We take into account the leading effects of axion self-interactions, showing that, even though these limit the number of axions produced within each cloud,a large number of superradiant axions become free of the black hole's gravitational potential and accumulate in the intergalactic medium or even in the host galaxy, depending on their escape velocity. This means that primordial black hole dark matter may lead to a sizeable astrophysical population of non-relativistic axions, with masses ranging from 0.1 eV to 1 MeV, depending on the primordial black hole mass and spin.We then show that if such axions couple to photons their contribution to the galactic and extragalactic background flux, mainly in the X-ray and gamma-ray band of the spectrum, is already beyond current observational limits for a large range of parameters that are, therefore, excluded. We finish by showing the prospects of the Athena X-ray telescope to further probe this co-existence of primordial black holes and axions.

On the interaction between ultralight bosons and quantum-corrected black holes

Both ultralight dark matter and exploring the quantum nature of black holes are all topics of great interest in gravitational wave astronomy at present. The superradiant instability allows an exotic compact object (ECO) to be surrounded by an ultralight boson cloud, which leads to the emission of gravitational waves and further triggers rich dynamical effects. In this paper, we study the gravitational effects of superradiant instabilities by calculating the energy fluxes of gravitational waves emitted from ultralight scalar dark matter fields by solving the Teukolsky equation in the background of a massive ECO phenomenologically described by a Kerr geometry with a reflective boundary condition at its physical boundary. We find that both the amplitude and phase of the reflectivity will either suppress or enhance the energy flux of GWs by several orders of magnitude if Mμ ≳ 0.5 where M and μ are the mass of ECO and boson, respectively. However, the modifications to energy flux are negligible if Mμ ≲ 0.5. Our results suggest that reflectivity will play a significant role in the near-horizon physics of ECO.

Spectral stability of near-extremal spacetimes

It has been suggested that the spectrum of quasinormal modes of rotating black holes is unstable against additional potential terms in the perturbation equation, as the operator associated with the equation is non-self-adjoint. We point out that a bilinear form has been constructed previously to allow a perturbation analysis of the spectrum, which was applied to study the quasinormal modes of weakly charged Kerr-Newman black holes [Phys. Rev. D 91, 044025 (2015)]. The proposed spectral instability should be restated as instability against potential terms that have an infinitesimal ``energy'' norm that is specifically defined by the type of inner products introduced by Jaramillo et al. and preserving the physical meaning of energy. We argue that it is necessary to address the stability of all previous mode analysis results to reveal their susceptibility to energetically infinitesimal perturbations. In particular, for near-extremal Kerr spacetime, we show that the spectrum of zero-damping modes, which have slow decay rates, is unstable (with order unity fractional change in decay rates) with fine-tuned modification of the potential. The decay rates are, however, always positive with energetically infinitesimal perturbations. If finite potential modifications are allowed near the black hole, it is possible to find superradiantly unstable modes, i.e., a ``black hole bomb'' without an explicit outer shell. For the zero-damping modes in near-extremal Reissner-Nordstr\"om--de Sitter black holes, which are relevant for the breakdown of strong cosmic censorship, we find that the corresponding spectrum is stable under energetically infinitesimal perturbations.

Next-to-leading-order solution to Kerr-Newman black hole superradiance

The superradiant instabilities of Kerr-Newman black holes with charged or uncharged massive spin-0 fields are calculated analytically to the next-to-leading order in the limit of $\alpha\sim r_g \mu \ll 1$. A missing factor of $1/2$ in the previous leading-order result is identified. The next-to-leading order result has a compact form and is in good agreement with existing numerical calculations. The percentage error increases with $\alpha$, from a few percent for $\alpha\sim 0.1$ to about $50\%$ for $\alpha\sim 0.4$. Massive neutral scalars too heavy to be produced with Kerr black hole superradiance may exist in the superradiant region of Kerr-Newman black holes.

Interplay of Kelvin-Helmholtz and superradiant instabilities of an array of quantized vortices in a two-dimensional Bose-Einstein condensate

We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose–Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin–Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI can resonantly couple to acoustic excitations propagating away in the bulk fluid on both sides. This makes the KHI rate to be effectively suppressed and other mechanisms to dominate: For finite and relatively small systems along the transverse direction, the instability involves a repeated superradiant scattering of sound waves off the vortex lattice; for transversally unbound systems, a radiative instability dominates, leading to the simultaneous growth of a localized wave along the vortex lattice and of acoustic excitations propagating away in the bulk. Finally, for slow velocities, where the KHI rate is intrinsically slow, another instability associated to the rigid lateral displacement of the vortex lattice due to the vicinity of the system’s boundary is found to dominate.

Scalar perturbation around rotating regular black hole: Superradiance instability and quasinormal modes

Black holes provide a natural laboratory to study particle physics and astrophysics. When black holes are surrounded by matter fields, there will be plenty of phenomena which can have observational consequences, from which we can learn about the matter fields as well as black hole spacetime. In this work, we investigate the massive scalar field in the vicinity of a newly proposed rotating regular black hole inspired by quantum gravity. We will especially investigate how this non-singular spactime will affect the superradiance instability and quasinormal modes of the scalar filed. We derive the superradiant conditions and the amplification factor by using the Matching-asymptotic Method, and the quasinormal modes are computed through Continued Fraction Method. In the Kerr limit, the results are in excellent agreements with previous research. We also demonstrate how the quasinormal modes will change as a function of black hole spin, regularity described by a parameter $k$ and scalar field mass respectively, with other parameters taking specific values.

Gregory-Laflamme and superradiance encounter black resonator strings

We construct novel black strings that are neither time-translation invariant, nor axisymmetric, nor translationally invariant in the string direction, but nevertheless have a helical Killing vector field. These solutions branch from the superradiant instability of D = 6 Myers-Perry black strings with equal angular momenta. We coin these solutions as black resonator strings and we find that they have more entropy than Myers-Perry black strings for the energies and angular momenta where both solutions coexist. We also construct Kaluza-Klein geons, which share the symmetries of black resonator strings, but are horizonless. Unlike in other superradiant systems, Kaluza-Klein geons are not the horizonless limit of black resonator strings and are instead entirely separate solutions.

Gregory-Laflamme encounters Superradiance

We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number — this is a ‘finite-m’ superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the ‘black resonator strings’ and ‘helical black strings’). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in D > 6 equal-spinning Myers-Perry black strings.

Mode stability results for the Teukolsky equations on Kerr–anti-de Sitter spacetimes

We prove that there are no non-stationary (with respect to the Hawking vectorfield), real mode solutions to the Teukolsky equations on all -dimensional subextremal Kerr–anti-de Sitter spacetimes. We further prove that stationary solutions do not exist if the black hole parameters satisfy the Hawking–Reall bound and . We conclude with the statement of mode stability which preludes boundedness and decay estimates for general solutions which will be proven in a separate paper. Our boundary conditions are the standard ones which follow from fixing the conformal class of the metric at infinity and lead to a coupling of the two Teukolsky equations. The proof relies on combining the Teukolsky–Starobinsky identities with the coupled boundary conditions. In the stationary case the proof exploits elliptic estimates which fail if the Hawking–Reall bound is violated. This is consistent with the superradiant instabilities expected in that regime.

Kerr black holes with synchronised Proca hair: lensing, shadows and EHT constraints

We investigate the gravitational lensing by spinning Proca stars and the shadows and lensing by Kerr black holes (BHs) with synchronised Proca hair, discussing both theoretical aspects and observational constraints from the Event Horizon Telescope (EHT) M87* and Sgr A* data. On the theoretical side, this family of BHs interpolates between Kerr-like solutions — exhibiting a similar optical appearance to that of Kerr BHs — to very non-Kerr like solutions, exhibiting exotic features such as cuspy shadows, egg-like shadows and ghost shadows. We interpret these features in terms of the structure of the fundamental photon orbits, for which different branches exist, containing both stable and unstable orbits, with some of the latter not being shadow related. On the observational side, we show that current EHT constraints are compatible with all such BHs that could form from the growth of the superradiant instability of Kerr BHs. Unexpectedly, given the (roughly) 10% error bars in the EHT data — and in contrast to their scalar cousin model —, some of the BHs with up to 40% of their energy in their Proca hair are compatible with the current data. We estimate the necessary resolution of future observations to better constrain this model.

From rotating to charged black holes and back again

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.

Lifetime of scalar cloud formation around a rotating regular black hole

Does circumventing the curvature singularity of the Kerr black hole affects the timescale of the scalar cloud formation around it? By definition, the scalar cloud, forms a gravitational atom with hydrogen-like bound states, lying on the threshold of a massive scalar field's superradiant instability regime (time-growing quasi-bound states) and beyond (time-decaying quasi-bound states). By taking a novel type of rotating hollow regular black hole proposed by Simpson and Visser which unlike its standard rivals has an asymptotically Minkowski core, we address this question. The metric has a minimal extension relative to the standard Kerr, originating from a single regularization parameter $\ell$, with length dimension. We show with the inclusion of the regularization length scale $\ell$ into the Kerr spacetime, without affecting the standard superradiant instability regime, the timescale of scalar cloud formation gets shorter. Since the scalar cloud after its formation, via energy dissipation, can play the role of a continuum source for gravitational waves, such a reduction in the instability growth time improves the phenomenological detection prospects of new physics because the shorter the time, the more astrophysically important.

Superradiant instability of dyonic Reissner–Nordström black holes

We investigate the superradiant instability of dyonic Reissner–Nordström (dRN) black holes with two charges under an electrically 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.

Ghost Instabilities in Self-Interacting Vector Fields: The Problem with Proca Fields.

Massive vector fields feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or an effective description of photons in a plasma. Here, we investigate vector fields with self-interactions by replacing the mass term in the Proca equation with a general potential. We show that this seemingly benign modification inevitably introduces ghost instabilities of the same kind as those recently identified for vector-tensor theories of modified gravity (but in this simpler, minimally coupled theory). It has been suggested that nonperturbative dynamics may drive systems away from such instabilities. We demonstrate that this is not the case by evolving a self-interacting Proca field on a Kerr background, where it grows due to the superradiant instability. The system initially evolves as in the massive case, but instabilities are triggered in a finite time once the self-interaction becomes significant. These instabilities have implications for the formation of condensates of massive, self-interacting vector bosons, the possibility of spin-one bosenovae, vector dark matter models, and effective models for interacting photons in a plasma.

Vortex String Formation in Black Hole Superradiance of a Dark Photon with the Higgs Mechanism.

Black hole superradiance, which only relies on gravitational interactions, can provide a powerful probe of the existence of ultralight bosons that are weakly coupled to ordinary matter. However, as a boson cloud grows through superradiance, nonlinear effects from interactions with itself or other fields may become important. As a representative example of this, we use nonlinear evolutions to study black hole superradiance of a vector boson that attains a mass, via a coupling to a complex scalar, through the Higgs mechanism. For the cases considered, we find that the superradiant instability can lead to a transient period where the scalar field reaches its symmetry restoration value, leading to the formation of closed vortex strings, the temporary disruption of the exponential growth of the cloud, and an explosive outburst of energy. After the cloud loses sufficient mass, the superradiant growth resumes, and the cycle repeats. Thus, the black hole will be spun down but, potentially, at a much lower rate compared to when nonlinear effects are unimportant and with the liberated energy going primarily into bosonic radiation instead of gravitational waves.

Superradiant evolution of the shadow and photon ring of Sgr A⋆

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 supermassive object Sgr A$^\star$ we show that both observables can vary appreciably over human timescales of a few years in the presence of superradiant instability, leading to signatures which are well within the reach of the Event Horizon Telescope for realistic observation times (but benefiting significantly from extended observation periods), and paving the way towards probing ultralight bosons in the $\sim 10^{-17}\,{\rm eV}$ mass range.