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 with it. We observe that for the low-frequency range of the scalar wave the superradiance scattering gets enhanced when the Lorentz-violating parameter $\ell$ takes the negative values and it reduces when values of $\ell$ are positive. The study of the black hole bomb issue reveals that for the negative values of $\ell$, the parameter space of the scalar field instability increase prominently, however, for its positive values, it shows a considerable reduction. We also tried to put constraints on the parameters contained in the Kerr-Sen-like black hole by comparing the deformation of the shadow produced by the black hole parameters with the observed deviation from circularity and the angular deviation from the $M87*$ data.
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…
The superradiance phenomena of massive bosons and fermions in the Kerr spacetime are studied in the Bargmann-Wigner formulation. In case of bi-spinor, the four independent components spinors correspond to the four bosonic freedom: one scalar and three vectors uniquely. The consistent description of the Bargmann-Wigner equations between fermions and bosons shows that the superradiance of the type with positive energy $(0<ω)$ and negative momentum near horizon $(p_{\rm H}<0)$ is shown not to occur. On the other hand, the superradiance of the type with negative energy $(ω<0)$ and positive momentu…
Recently Van Putten has suggested that superradiance of magnetosonic waves in a toroidal magnetosphere around a Kerr black hole may play a role in the central engine of gamma-ray bursts. In this context, he computed (in the WKB approximation) the superradiant amplification of scalar waves confined to a thin equatorial wedge around a Kerr hole and found that the superradiance is higher than for radiation incident over all angles. This paper presents calculations of both spin-0 (scalar) superradiance (integrating the radial equation rather than using the WKB method) and and spin-1 (electromagnet…
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…
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 …
Superradiance in black hole spacetimes can trigger instabilities. Here we show that, due to superradiance, small Kerr-anti-de Sitter black holes are unstable. Our demonstration uses a matching procedure, in a long wavelength approximation.
We consider the propagation of a generic scalar field around a rotating and charged black hole. Using the partial wave method, we find, numerically, the total and partial absorption cross sections for different incidence angles. We investigate the low- and high-frequency limits, finding semi-analytical approximations for the absorption cross section, which we compare with our numerical results. Finally, we consider the superradiant regime, showing that, for charged fields, planar waves can be superradiantly scattered.
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 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.
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…
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 study the absorption of plane waves by Kerr black holes. We calculate the absorption cross section: the area of the black hole shadow at a finite wavelength. We present a unified picture of the absorption of all massless bosonic fields, focussing on the on-axis incidence case. We investigate the spin-helicity effect, arising from a coupling between dragging of frames and the helicity of a polarized wave. We introduce and calibrate an extended sinc approximation which provides new quantitative data on the spin-helicity effect in strong-field gravity.
We consider a Lorentz violating non-commutating Kerr-like spacetime and studied the superradiance effect and the shadow cast by the back hole. We extensively study the different aspects of the black hole associated with a generalized Kerr-like spacetime metric endowed with the corrections licked with Lorentz violation and non-commutativity effect jointly. We investigate the superradiance effect, deviation of shape, and size of the ergosphere, energy emission rate, and black hole shadow in this generalized situation and study their variation taking different admissible values of Lorentz violati…
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.
In this work we investigate validity of the weak form of the cosmic censorship conjecture in the interaction of Kerr-Sen black holes with neutral test fields. Previous studies of the Klein-Gordon equation on Kerr-Sen background imply that superradiance occurs for scalar fields. We show that scalar fields can overspin a nearly extremal black hole into a naked singularity, but the modes that could overspin an extremal black hole are not absorbed due to superradiance. From Kerr analogy one can naively expect superradiance to be absent for fermionic fields. In such a case overspinning becomes gene…
Kerr black holes with synchronised hair [arXiv:1403.2757, arXiv:1603.02687] are a counter example to the no hair conjecture, in General Relativity minimally coupled to simple matter fields (with mass $μ$) obeying all energy conditions. Since these solutions have, like Kerr, an ergoregion it has been a lingering possibility that they are afflicted by the superradiant instability, the same process that leads to their dynamical formation from Kerr. A recent breakthrough [arXiv:1711.08464] confirmed this instability and computed the corresponding timescales for a sample of solutions. We discuss ho…
Superradiance and Quasinormal Modes of Massive Scalar Fields around Kerr Black Holes in Einstein-Maxwell-Dilaton-Axion Theory with Perfect Fluid Dark Matter
Division of Physical Science, Faculty of Science, Prince of Songkla University（宋卡王子大学理学院物理科学系）
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…
We study scalar test-field perturbations on top of a Kerr--black-bounce background, i.e. a family of rotating regular black holes and/or rotating traversable wormholes that can mimic Kerr black holes. We compute the quasi-normal modes for a massless field in both the regular black holes and wormhole branches, confirming the stability of the former and identifying a set of growing modes that renders the latter unstable. We further compute the superradiance amplification factors, for massless and massive fields, in the regular black hole branch, confirming that these objects superradiate, though…
Dark radiation from Kerr primordial black holes: the role of superradiance
College of Sciences, Northeastern University（东北大学理学院）；Liaoning Key Laboratory of Cosmology and Astrophysics（辽宁省宇宙学与天体物理重点实验室）；MOE Key Laboratory of Data Analytics and Optimization for Smart Industry（教育部智能工业数据分析与优化重点实验室）；National Frontiers Science Center for Industrial Intelligence and Systems Optimization（国家工业智能与系统优化前沿科学中心）
We discuss the late-time behaviour of a dynamically perturbed Kerr black hole. We present analytic results for near extreme Kerr black holes that show that the large number of virtually undamped quasinormal modes that exist for nonzero values of the azimuthal eigenvalue m combine in such a way that the field oscillates with an amplitude that decays as 1/t at late times. This prediction is verified using numerical time-evolutions of the Teukolsky equation. We argue that the observed behaviour may be relevant for astrophysical black holes, and that it can be understood in terms of the presence o…
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…
Superradiant scattering of linear spin $s=0,\pm 1,\pm 2$ fields on Kerr black hole background is investigated in the time domain by integrating numerically the homogeneous Teukolsky master equation. The applied numerical setup has already been used in studying long time evolution and tail behavior of electromagnetic and metric perturbations on rotating black hole background [arXiv:1905.09082v3]. To have a clear setup the initial data is chosen to be of the compact support, while to optimize superradiance the frequency of the initial data is fine tuned. Our most important finding is that the ra…
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…
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 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 metri…
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…
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…
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…
Classical Censorship permits AdS$_5$-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 $2\sqrt{2}L$, where $L$ is the asymptotic curvature scale. One might suppose that the most rapidly rotating AdS$_5$-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 al…
In this work we investigate if the interaction of the Kerr-Taub-NUT spacetime with test scalar and neutrino fields can lead to the destruction of the event horizon. It turns out that both extremal and nearly extremal black holes can be destroyed by scalar and neutrino fields if the initial angular momentum of the spacetime is sufficiently large relative to its mass and NUT charge. This is the first example in which a classical field satisfying the null energy condition can actually destroy an extremal black hole. For scalar fields, the modes that can lead to the destruction of the horizon are …
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.
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…
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 consider the stationary metrics that have both the black hole and the ergoregion. The class of such metric contains, in particular, the Kerr metric. We study the Cauchy problem with highly oscillatory initial data supported in a neighborhood inside the ergoregion with some initial energy $E_0$. We prove that when the time variable $x_0$ increases this solution splits into two parts: one with the negative energy $-E_1$ ending at the event horizon in a finite time, and the second part, with the energy $E_2=E_0+E_1>E_0$, escaping, under some conditions, to the infinity when $x_0\rightarrow +\i…
We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M μ\lesssim 0.5$. For a fast rotating hole ($a …
We numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate non-uniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we …
We calculate the self-force acting on a charged particle on a circular geodesic orbit in the equatorial plane of a rotating black hole. We show by direct calculation that the dissipative self-force balances with the sum of the flux radiated to infinity and through the black hole horizon. Prograde orbits are found to stimulate black hole superradiance, but we confirm that the condition for floating orbits cannot be met. We calculate the conservative component of the self-force by application of the mode sum regularization method, and we present a selection of numerical results. By numerical fit…
This dissertation aims at studying the braneworld models in the context proposed by Randall and Sundrum. The focus is on the spin-0 perturbations in the Kerr space-time as a 4-dimensional braneworld. The work deals the main aspects of Einstein General Relativity as well as perturbations of black holes metrics. We also review the Randall-Sundrum models and their motivations and attempts to describe braneworld black holes. In the end the Kerr-Randall-Sundrum black string scalar perturbation and superradiance are obtained.
Highly spinning Kerr black holes with masses $M = 1 - 100\ M_{\odot}$ are subject to an efficient superradiant instability in the presence of bosons with masses $μ\sim 10^{-10} - 10^{-12}\ {\rm eV}$. We observe that this matches the effective plasma-induced photon mass in diffuse galactic or intracluster environments ($ω_{\rm pl} \sim 10^{-10} - 10^{-12}\ {\rm eV}$). This suggests that bare Kerr black holes within galactic or intracluster environments, possibly even including the ones produced in recently observed gravitational wave events, are unstable to formation of a photon cloud that may …
We investigate the ringdown waveform and reflectivity of a Lifshitz scalar field around a fixed Schwarzschild black hole. The radial wave equation is modified due to the Lorentz breaking terms, which leads to a diversity of ringdown waveforms. Also, it turns out that Lifshitz waves scattered by the Schwarzschild black hole exhibits superradiance. The Lorentz breaking terms lead to superluminal propagation and high-frequency modes can enter and leave the interior of the Killing horizon where negativity of energy is not prohibited. This allows the Lifshitz waves to carry out additional positive …
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…
