We study the superradiance amplification factor (SAF) for a charged massive scalar wave scattering off small and slowly rotating Kerr-Newman black holes in $f(R)$ gravity immersed in asymptotically flat and de-Sitter spacetimes. We employ the \emph{``analytical asymptotic matching''} approximation technique which is valid in low frequency regime where the Compton wavelength of the propagating particle is much larger than the size of the black hole. The $f(R)$-Kerr-Newman family solution induces an extra distinguishable effect on the contribution of the black hole's electric charge to the metric and that in turn affects the SAFs and their frequency ranges. While our analysis are general, we present the numerical results for the Starobinsky and Hu-Sawicki $f(R)$ models of gravity as our working examples. In the case of asymptotically flat spacetime, the SAFs predicted in Starobinsky $f(R)$ model are not distinguishable from those of GR while for Hu-Sawicki model the SAFs can be weaker or stronger than those of GR within the frequency parameters space. In the case of asymptotically de-Sitter spacetime, the superradiance scattering may not either occur in Starobinsky model or has a weaker chance compared to GR while in Hu-Sawicki model the results of SAFs and their frequency regimes are different from the standard ones.
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 $α<0$ and will be weakened with $α>0$. Moreover, by addressing the black hole bomb issue, we extract an improved bound in the instability regime indicating that $α<0$ incre…
Institute for Basic Science (IBS)（韩国基础科学研究所）；Cosmology, Gravity, and Astroparticle Physics Group, Center for Theoretical Physics of the Universe（宇宙学、引力与天体物理组，宇宙理论物理中心）；Center for Geometry and Physics（几何与物理中心）
We discuss the relation between the superradiance phenomenon and the instability of rotating black holes in higher dimensions. In particular, we point out that the superradiant instability of a massless scalar field around a simply rotating Kerr-adS black hole implies the gravitational instability of that black hole for tensor-type perturbations.
It is shown that Chern-Simons gravities in $2n+1$ dimensions admit solutions described by the same lapse function which describes the BTZ black hole in the $n=1$ case. This has been carried out explicitly for $n=1,2,3$. Moreover, it is seen that these solutions are unique.
We study the superradiant scattering of gravitational waves by a nearly extremal black hole (dimensionless spin $a=0.99$) by numerically solving the full Einstein field equations, thus including backreaction effects. This allows us to study the dynamics of the black hole as it loses energy and angular momentum during the scattering process. To explore the nonlinear phase of the interaction, we consider gravitational wave packets with initial energies up to $10%$ of the mass of the black hole. We find that as the incident wave energy increases, the amplification of the scattered waves, as well …
Superradiance is known as a wave amplification process caused by rotating or charged black holes. We argue that the superradiance of stationary black holes in asymptotically AdS spacetimes can be characterized by the ability of energy extraction. Specifically, we demonstrate that energy can be extracted from Reissner-Nordström-AdS$_4$ and Kerr-AdS$_4$ under appropriate time-dependent boundary conditions at conformal boundaries. This indicates that energy can be extracted from thermal states dual to these black holes by applying appropriate time-dependent sources. We also show that the energy e…
The superradiant scattering of a scalar field with frequency and angular momentum (ω,m) by a near-extreme Kerr black hole with mass and spin (M,J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (ω,m,M,J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conject…
We studied the superradiance effect of a charge black hole immersed in an expanding Universe. We considered a test massive charged scalar field scattered off the horizon of the charge McVittie black hole. We carried out a detailed analysis of the electric energy extracted from the horizon of McVittie black hole in two different epochs of the expansion of the Universe, the dust dominated and radiation dominated epochs. We found that we have the superradiance effect in both epochs of the expansion of the Universe. Our study also provides evidence that we have extraction of energy from the horizo…
Black holes have turned into cosmic laboratories to search for ultra-light scalars by virtue of the superradiant instability. In this paper we present a detailed study of the impact of the superradiant evolution on the black hole shadow and investigate the exciting possibility to explore it with future observations of Very Long Baseline Interferometry. We simulated the superradiant evolution numerically, in the adiabatic regime, and derived analytic approximations modelling the process. Driven by superradiance, we evolve the black hole shadow diameter and (i) find that it can change by a few $…
It is shown that the superradiance modes always exist in the radiation by the $(4+n)$-dimensional rotating black holes. Using a Bekenstein argument the condition for the superradiance modes is shown to be $0 < ω< m Ω$ for the scalar, electromagnetic and gravitational waves when the spacetime background has a single angular momentum parameter about an axis on the brane, where $Ω$ is a rotational frequency of the black hole and $m$ is an azimuthal quantum number of the radiated wave.
We discuss the conditions under which plane electromagnetic and gravitational waves can be amplified by a rotating black hole due to superradiant scattering. We show, in particular, that amplification can occur for low-frequency waves with an incidence angle parametrically close to 0 (or $π$) with respect to the black hole spin axis and with a parametrically small left (or right) polarization. This is the case of the radiation emitted by a spinning electric/magnetic dipole or gravitational quadrupole orbiting a black hole companion at large radius and co-rotating with the latter. This can yiel…
We present an exact expression for the quasinormal modes of acoustic disturbances in a rotating 2+1 dimensional sonic black hole (draining bathtub fluid flow) in the low frequency limit and evaluate the adiabatic invariant proposed by Kunstatter. We also compute,via Bohr-Sommerfeld quantization rule the equivalent area spectrum for this acoustic black hole, and we compute the superradiance phenomena for pure spinning 2+1 black holes.
Black Hole Superradiance of Interacting Multi-Field
International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（国际理论物理中心亚太分部，中国科学院大学）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学前沿科学与数学学院，杭州高等研究院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Taiji Laboratory for Gravitational Wave Universe, University of Chinese Academy of Sciences（中国科学院大学太极引力波宇宙实验室）
We study the quantum analogue of the classical process of superradiance for a massless charged scalar field on a static charged black hole space-time. We show that an "in" vacuum state, which is devoid of particles at past null infinity, contains an outgoing flux of particles at future null infinity. This radiation is emitted in the superradiant modes only, and is nonthermal in nature.
Focusing on the rotating black hole (BH) surrounded by the anisotropic fluid matters; radiation, dust, and dark matter, we study the massive scalar superradiant scattering and the stability in the Kiselev spacetime. Superradiance behavior is dependent on the intensity parameter of the anisotropic matter $K$ in the Kiselev spacetime. By adopting the manifest of low-frequency and low-mass for the scalar perturbation, we find $K<0$ enhances the superradiance scattering within the broader frequency range, compared to $K=0$ while $K>0$ suppresses within the narrower frequency range. As a result, th…
We investigate the stability of $D$ dimensional singly rotating Myers-Perry-AdS black holes under superradiance against scalar field perturbations. It is well known that small four dimensional rotating or charged Anti-de Sitter (AdS) black holes are unstable against superradiance instability of a scalar field. Recent works extended the existence of this instability to five dimensional rotating charged AdS black holes or static charged AdS black holes in arbitrary dimensions. In this work we analytically prove that, rotating small AdS black holes in arbitrary dimensions also show superradiance …
We consider the definition of the Boulware and Hartle-Hawking states for quantum fields on black hole space-times. The properties of these states on a Schwarzschild black hole have been understood for many years, but neither of these states has a direct analogue on a Kerr black hole. We show how superradiant modes play an important role in the definition of quantum states on Kerr. Superradiance is also present on static black hole space-times, in particular for a charged scalar field on a Reissner-Nordstrom black hole. We explore whether analogues of the Boulware and Hartle-Hawking states exis…
Einstein gravities in general dimensions coupled to a cosmological constant and extended with quadratic curvature invariants admit a variety of black holes that may asymptote to Minkowski, anti-de Sitter or Lifshitz spacetimes. We adopt the Wald formalism to derive an explicit formula for calculating the thermodynamical first law for the static black holes with spherical/toric/hyperbolic isometries in these theories. This allows us to derive/rederive the first laws for a wide range of black holes in literature. Furthermore, we construct many new exact solutions and obtain their first laws.
Ongoing observations in the strong-field regime are in optimal agreement with general relativity, although current errors still leave room for small deviations from Einstein's theory. Here we summarise our recent results on superradiance of scalar and electromagnetic test fields in Kerr-like spacetimes, focusing mainly on the Konoplya--Zhidenko metric. We observe that, while for large deformations with respect to the Kerr case superradiance is suppressed, it can be nonetheless enhanced for small deformations. We also study the superradiant instability caused by massive scalar fields, and we pr…
In this article, the behaviour of a charged and massive scalar field around a global monopole swallowed by a Reissner-Nordström-Anti-de Sitter (RN-AdS) black hole is investigated by considering the Klein-Gordon equation in this geometry. The superradiance phenomenon and instability behaviour of the black hole against charged scalar perturbations are studied for both an RN-AdS case and also for an RN black hole surrounded by a reflective mirror, i.e., the black hole bomb case. The effects of the monopole on these cases are discussed analytically and also with the help of several graphs in detai…
Recent strong-field regime tests of gravity are so far in agreement with general relativity. In particular, astrophysical black holes appear all to be consistent with the Kerr spacetime, but the statistical error on current observations allows for small yet detectable deviations from this description. Here we study superradiance of scalar and electromagnetic test fields around the Kerr-like Konoplya--Zhidenko black hole and we observe that for large values of the deformation parameter superradiance is highly suppressed with respect to the Kerr case. Surprisingly, there exists a range of small …
We consider a superradiance effect around rotating dilatonic black holes. We analyze two cases: one is an exact solution with the coupling constant $α=\sqrt{3}$, which effective action is reduced from the 5-dimensional Kaluza-Klein theory, and the other is a slowly rotating dilatonic black holes with arbitrary coupling constant. We find that there exists a critical value ($α\sim 1$), which is predicted from a superstring model, and the superradiant emission rate with coupling larger than the critical value becomes much higher than the Kerr-Newman case ($α=0$) in the maximally charged limit. Co…
The propagation of electromagnetic plane waves with negative phase velocity (NPV) in the ergosphere of a rotating black hole has recently been reported. A comparison of NPV propagation and superradiance is presented. We show that, although both phenomenons involve negative energy densities, there are two significant differences between them.
We consider scalar field perturbations of the asymptotically Gödel 5-dimensional charged rotating black holes with two equal angular momenta. It is shown that the spectrum of proper oscillations of the perturbation includes superradiant unstable modes. The reason for the instability is the confining Dirichlet boundary condition at the asymptotically far region of the Gödel Universe. The confining box makes superradiant modes extract rotational energy from the black hole and, after repeated reflections from the black hole, grow unboundedly. A similar instability takes place for rotating black h…
We consider extended cosmological gravities with Ricci tensor and scalar squared terms in diverse dimensions. These theories admit solutions of Einstein metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass and entropy vanish at the critical point. We perform linearized analysis around the black holes and show that in general the spectrum consists of the usual spin-2 massless and ghost massive modes. We demonstrate that there is no exponentially-growing tachyon mode in the black holes. At the critical point, the massless spin-2 modes have zero energy whilst the massive s…
Bargmann-Wigner equations are formulated to represent bosonic fields in terms of fermionic fields in curved spacetime. The superradiance phenomena of bosons and fermions in rotating black hole spacetime are studied in the Bargmann-Wigner formulation. As a result of the consistent description between scalar bosons and spinor fermions, superradiance phenomena of the type of positive frequency $(0<ω)$ and negative momentum near horizon $(p_{H}<0)$ are shown not to occur.
We explore superradiance for Alfvén waves (Alfvénic superradiance) in an axisymmetric rotating magnetosphere of a Kerr black hole within the force-free approximation. On the equatorial plane of the Kerr spacetime, the Alfvén wave equation is reduced to a one-dimensional Schrödinger-type equation by separating variables of the wave function and introducing a tortoise coordinate mapping the inner and outer light surfaces to $-\infty$ and $+\infty$, respectively, and we investigate a wave scattering problem for Alfvén waves. An analysis of the asymptotic solutions of the wave equation and the con…
We investigate the effect of superradiance shielding for the analogue rotating black holes simulated by optical vortices by calculating the radial motion of massless particles in such spacetime background. We add the conditions $E<LΩ_{r_{e}}$ and $L>0$ to judge the classically forbidden region of superradiance. It is found that the superradiance forbidden region exists near the static limit inside the ergosphere,which will limit the classical Penrose process for the particles with some specific energies and angular momenta. Once these particles satisfying the superradiance conditions aremeasur…
In gravitational thermodynamics, the entropy of a black hole with distinct surface gravities can be evaluated in a microcanonical ensemble. At the $WKB$ level, the entropy becomes the negative of the Euclidean action of the constrained instanton, which is the seed for the black hole creation in the no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite universal formula in Euclidean quantum gravity that the entropy of a nonrotating black hole is one quarter the sum of the products of the Euler characteristics and the areas of the horizons. For Lovelock gravity, the entropy an…
We investigated the superradiance and stability of the novel 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 consant $α$ 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 live beyond the superradiance condition and the imaginary parts are all negative. Therefo…
An inhomogeneous pseudo-scalar field configuration behaves like an optically active medium. Consequently, if a light ray passes through an axion cloud surrounding a Kerr black hole, it may experience a polarization-dependent bending. We explore the size and relevance of such effect considering both the QCD axion and a generic axion-like particle.
In this paper we invstigate the possibility of the acoustic analogue of a phenomenon like superradiance, that is, the amplification of a sound wave by reflection from the ergo-region of a rotating acoustic black hole in the fluid "draining bathtub" model in the presence of a desclination be amplified or reduced in agreement with the value of the deficit angle.
We calculate the statistical entropy of a rotating hairy black hole by taking into account superradiant modes in the brick wall method. The UV cutoff is independent of the gravitational hair, which gives the well-defined area law of the entropy. It can be shown that the angular momentum and the energy of matter field depend on the gravitational hair. For the vanishing gravitational hair, it turns out that the energy for matter is related to both the black hole mass and the black hole angular momentum whereas the angular momentum for matter field is directly proportional to the angular momentum…
We analyze the amplification due to so-called superradiance from the scattering of pulses off rotating black holes as a numerical time evolution problem. We consider the "worst possible case" of scalar field pulses for which superradiance effects yield amplifications $< 1%$. We show that this small effect can be isolated by numerically evolving quasi-monochromatic, modulated pulses with a recently developed Teukolsky code. The results show that it is possible to study superradiance in the time domain, but only if the initial data is carefully tuned. This illustrates the intrinsic difficulties …
We examine the black hole bomb model which consists of a rotating black hole of five-dimenensional minimal ungauged supergravity and a reflecting mirror around it. For low-frequency scalar perturbations, we find solutions to the Klein-Gordon equation in the near-horizon and far regions of the black hole spacetime. To avoid solutions with logarithmic terms, we assume that the orbital quantum number $ l $ takes on nearly, but not exactly, integer values and perform the matching of these solutions in an intermediate region. This allows us to calculate analytically the frequency spectrum of quasin…
Vortices and black holes set the scene for many interesting dynamical processes in physics. Here, we study the dynamical instability of quantised vortices and rotational superradiance around rotating black holes, illustrating in the process that the same physics is at play in these two seemingly disparate phenomena. We also compare the instability of the vortex to the black hole bomb instability, which occurs for massive scalar fields in the Kerr spacetime. Taking inspiration from the analogy between black hole bomb modes and the hydrogen spectrum, the vortex instability is compared with nucle…
We construct hairy black hole solutions that merge with the anti-de Sitter (AdS$_4$) Reissner-Nordström black hole at the onset of superradiance. These hairy black holes have, for a given mass and charge, higher entropy than the corresponding AdS$_4$-Reissner-Nordström black hole. Therefore, they are natural candidates for the endpoint of the charged superradiant instability. On the other hand, hairy black holes never dominate the canonical and grand-canonical ensembles. The zero-horizon radius of the hairy black holes is a soliton (i.e. a boson star under a gauge transformation). We construct…
Rotating small AdS black holes exhibit the superradiant instability to low-frequency scalar perturbations, which is amenable to a complete analytic description in four dimensions. In this paper, we extend this description to all higher dimensions, focusing on slowly rotating charged AdS black holes with a single angular momentum. We divide the spacetime of these black holes into the near-horizon and far regions and find solutions to the scalar wave equation in each of these regions. Next, we perform the matching of these solutions in the overlap between the regions, by employing the idea that …
The changes a (negative) tidal charge causes at the phenomenon of superradiance which occurs around rotating black holes are investigated. This is made by computing the amplification factors of massless scalar waves being scattered by the black hole. It is shown that the increase of the tidal charge intensity leads to a considerable enhancement of energy extraction from near-extreme black holes. Such improvement results from the fact that extreme black holes with more negative tidal charges spin faster. Maximum amplification decreases with the increase of the tidal charge intensity if the angu…
We study slowly rotating black hole solutions in the six independent theories of Einstein Quartic Gravity (EQG) in four dimensions. Unlike in the static case for which all six theories yield the same solution, for rotating black holes we obtain distinct results for five out of the six theories. Working to leading order in the rotation parameter, we find that the equations characterizing these black holes can be reduced to second order for each theory, similar to what has already been done for Einstein Cubic Gravity. We construct approximate and numerical solutions to these equations, and study…
A Kerr-Sen-like black hole solution results from Einstein-bumblebee gravity. It contains a Lorentz violating (LV) parameter that enters when the bumblebee field receives vacuum expectation value through a spontaneously breaking of the symmetry of the classical action. The geometrical structure concerning the singularity of this spacetime is studied with reference to the parameters involved in the Kerr-Sen-like metric. We introduce this Einstein-bumblebee modified gravity to probe the role of spontaneous Lorentz violation on the superradiance scattering phenomena and the instability associated …
Using the Kerr-Schild formalism to solve the Einstein-Maxwell equations, we study energy transport due to time-dependent electromagnetic perturbations around a Kerr black hole, which may work as a mechanism to illuminate a disk located on the equatorial plane. For such a disk-hole system it is found that the energy extraction from the hole can occur under the well-known superradiance condition for wave frequency, even though the energy absorption into the hole should be rather dominant near the polar region of the horizon. We estimate the efficiency of the superradiant amplification of the dis…
By choosing an appropriate vielbein basis, we obtain a class of spherically-symmetric solutions in $f(T)$ gravities. The solutions are asymptotic to Minkowski spacetimes with leading falloffs the same as those of the Schwarzschild black hole. In general, these solutions have branch-cut singularities in the middle. For appropriately chosen $f(T)$ functions, extremal black holes can also emerge. Furthermore, we obtain wormhole configurations whose spatial section is analogous to an Ellis wormhole, but $-g_{tt}$ runs from 0 to 1 as the proper radial coordinate runs from $-\infty$ to $+\infty$. Th…
We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by…
We investigate the absorption of a massive and charged scalar field in a Reissner-Nordström background. We compare our numerical results for the absorption cross section, obtained for arbitrary frequencies, with the low- and high-frequency limits. We find, in particular, that the total absorption cross section can be negative, showing that planar scalar waves can be superradiantly amplified by black holes.
