In this paper, the behaviour of a charged massive scalar test field in the background of a Kerr-Sen black hole is investigated. A kind of stationary solutions, dubbed scalar clouds, are obtained numerically and expressed by the existence lines in the parameter space. We show that for fixed background and a given set of harmonic indices, the mass and charge of the scalar clouds are limited in a finite region in the parameter space of the scalar field. Particularly, the maximum values of the mass and charge of the clouds around extremal Kerr-Sen black holes are independent of the angular velocity of the black hole, whereas those in the extremal Kerr-Newman background depend on the angular velocity. In addition, it is demonstrated that, as the static limit of Kerr-Sen black hole, Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole can not support scalar cloud.
Massive complex scalar fields can form bound states around Kerr black holes. These bound states -- dubbed scalar clouds -- are generically non-zero and finite on and outside the horizon; they decay exponentially at spatial infinity, have a real frequency and are specified by a set of integer "quantum" numbers (n,l,m). For a specific set of these numbers, the clouds are only possible along a 1-dimensional subset of the 2-dimensional parameter space of Kerr black holes, called an existence line. In this paper we make a thorough investigation of the scalar clouds due to neutral (charged) scalar f…
Nonlinear electroweak sphaleron clouds around Kerr black holes
Universidade de Aveiro（阿威罗大学）；Centre for Research and Development in Mathematics and Applications (CIDMA)（数学与应用数学研究与发展中心）；Universität Oldenburg（奥尔登堡大学）；U. Federal do Pará（帕拉联邦大学）
It is shown that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. To that end, we solve analytically the Klein-Gordon wave equation for a stationary charged massive scalar field in the background of a near-extremal Kerr-Newman black hole. In particular, we derive a simple analytical formula which describes the physical properties of these stationary bound-state resonances of the charged massive scalar fields in the Kerr-Newman black-hole spacetime.
Q-balls are regular extended `objects' that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces - …
Under certain conditions sound waves in fluids experience an acoustic horizon with analogue properties to those of a black hole event horizon. In particular, a draining bathtub-like model can give rise to a rotating acoustic horizon and hence a rotating black hole (acoustic) analogue. We show that sound waves, when enclosed in a cylindrical cavity, can form stationary waves around such rotating acoustic black holes. These acoustic perturbations display similar properties to the scalar clouds that have been studied around Kerr and Kerr-Newman black holes; thus they are dubbed acoustic clouds. W…
Recent studies have made key progress on the black hole/solitonic solutions of the Einstein-Proca system. Firstly, fully non-linear dynamical evolutions of the Kerr black hole superradiant instability, triggered by a Proca field, have shown the formation of a new equilibrium state, a spinning black hole with synchronised Proca hair. Secondly, non-linear evolutions of spinning Proca stars have established that they are dynamically stable, unlike their scalar cousins. Thirdy, separability of the Proca equation on the Kerr background has been achieved. Motivated by these results, in this paper we…
We study analytically the Klein-Gordon wave equation for stationary massive scalar fields linearly coupled to spinning Kerr black holes. In particular, using the WKB approximation, we derive a compact formula for the discrete spectrum of scalar field masses which characterize the stationary composed Kerr-black-hole-massive-scalar-field configurations in the large-coupling regime $Mμ\gg1$ (here $M$ and $μ$ are respectively the mass of the central black hole and the proper mass of the scalar field). We confirm our analytically derived formula for the Kerr-scalar-field mass spectrum with numerica…
In this paper we have took reissner nordstrom blackhole with cloud of strings and surrounds it with quintessence. we processed the metric through newman janis algorithm to get its rotating counterpart. the blackhole in study now is a roating charged blackhole with clouds of string surrounded by quintessence. we studied its nature of effective potential and unstable photon orbits. Finally we have plotted the blackhole shadow for various variable profiles.
Scalar and gravitational perturbations on Kerr-anti-de Sitter (Kerr-AdS) black holes have been addressed in the literature and have been shown to exhibit a rich phenomenology. In this paper we complete the analysis of bosonic fields on this background by studying Maxwell perturbations, focusing on superradiant instabilities and vector clouds. For this purpose, we solve the Teukolsky equations numerically, imposing the boundary conditions we have proposed in\cite{Wang:2015goa} for the radial Teukolsky equation. As found therein, two Robin boundary conditions can be imposed for Maxwell fields on…
We use the continued fraction method to determine the eigenfrequencies associated with a scalar field around a Kerr-like black hole. The Kerr-like metric considered in this article is a subclass of the general parametrization of axisymmetric black holes proposed by Konoplya, Rezzolla and Zhidenko. In addition to its mass $M$ and specific angular momentum $a$, the black hole depends on a third parameter $η$, called the deformation parameter. We investigate how the deformation parameter affects the quasinormal modes and the quasibound states of a massive scalar field around the black hole. In pa…
Massive bosons in the vicinity of Kerr-Newman black holes can form pure bound states when their phase angular velocity fulills the synchronisation condition, i.e. at the threshold of superradiance. The presence of these stationary clouds at the linear level is intimately linked to the existence of Kerr black holes with synchronised hair at the non-linear level. These configurations are very similar to the atomic orbitals of the electron in a hydrogen atom. They can be labeled by four quantum numbers: $n$, the number of nodes in the radial direction; $\ell$, the orbital angular momentum; $j$, t…
Numerical analysis of dark matter axion-like cloud in the vicinity of rotating black hole has been performed. The model where axion-like scalar field is non-trivially coupled to Maxwell field is studied in the spacetime of Kerr black hole in uniform magnetic field and in Kerr-Newman one. The dependence of scalar mass and black hole angular momentum on accumulation of axion dark matter cloud was given. It was revealed that condensation of the dark matter clouds is preferable for a very small mass of axion.
In this paper, an exact solution of Kerr black hole surrounded by a cloud of strings in Rastall gravity is obtained by Newman-Janis algorithm without complexification, and the influence of the string parameter $a_0$ on the black hole thermodynamics is studied. Furthermore, according to this black hole solution, we investigate the effect of a cloud of strings on gravitational deflection of massive particles. For a receiver and a source at infinite distance from the lens object, we use an osculating Riemannian manifold method. While the distance is finite, we apply the generalized Jacobi metric …
In this paper, we study a physical system that is composed of massive charged scalar field linearly coupled to a charged rotating Kerr-Newman black hole. Given the parameters of black hole and a specific set of "quantum" numbers, the parameter space of the scalar field, which is a plane spanned by its mass and charge, is divided into five partitions by three simple constraint lines and the existence line of scalar clouds. The physical properties of the system in these partitions are presented. It is found that superradiant instability may be possibly caused only in two of the partitions. In pa…
Scalar fields around compact objects are of interest for scalar-tensor theories of gravity and dark matter models consisting of a massive scalar, e.g. axions. We study the behaviour of a scalar field around a Kerr black hole with non trivial asymptotic boundary conditions - both non zero density and non zero angular momentum. Starting from an initial radially homogeneous configuration, a scalar cloud is accreted, which asymptotes to known stationary configurations over time. We study the cloud growth for different parameters including black hole spin, scalar field mass, and the scalar field de…
Assuming that a particle source is at rest in a locally non-rotating frame on the equatorial plane of the Kerr-Sen black hole, we investigate the escape of the massless particle and massive particle from the black hole to spatial infinity. We calculate the escape probabilities of the emitted particles. We find that the angular momentum of the Kerr-Sen black hole boosts the escape probabilities near the horizon of the extreme Kerr-Sen black hole; however the angular momentum of the Kerr-Sen black hole suppresses the escape probabilities near the horizon of the non-extreme Kerr-Sen black hole. W…
The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein--Maxwell gravity (the Kerr--Newman solution) and low-energy heterotic string theory (the Kerr--Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black ho…
We study solutions of the Einstein-Skyrme model. Firstly we consider test field Skyrmions on the Kerr background. These configurations -- hereafter dubbed Skerrmions -- can be in equilibrium with a Kerr black hole (BH) by virtue of a synchronisation condition. We consider two sectors for Skerrmions. In the sector with non-zero baryon charge, Skerrmions are akin to the known Skyrme solutions on the Schwarzschild background. These `topological' configurations reduce to flat spacetime Skyrmions in a vanishing BH mass limit; moreoever, they never become "small" perturbations on the Kerr background…
Relativistic Tidal Transitions of Saturated Kerr Boson Clouds
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, CAS（中国科学院新疆天文台射电天文技术国家重点实验室）；College of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Xinjiang Key Laboratory of Radio Astrophysics（新疆射电天体物理重点实验室）
Behaviour of singularities of the rotating black holes under an arbitrary boost is considered on the basis of a complex representation of the Kerr theorem. We give a simple algorithm allowing to get explicit expressions for the metric and the position of the singularities for arbitrary direction and magnitude of the boost, including the ultrarelativistic case. The non-smoothness of the ultrarelativistic limit is discussed. The Kerr-Sen BH-solution to low energy string theory is also analyzed.
We study the entropy of Kerr-Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non leading corrections to the area law are obtained.
We first calculate equations of motion for particles in the Kerr-Sen-de Sitter black hole spacetime. Then in the eikonal regime, we analytically obtain the quasi-normal resonant modes of massless neutral scalar field perturbation and find its imaginary part to be characterized by the surface gravity of the near-extremal Kerr-Sen-de Sitter black hole with Cauchy horizon approaching the event horizon. We further show that the Penrose strong cosmic censorship conjecture is thus respected in this spacetime with dilaton scalar field and axion pseudoscalar field.
It was reported that Kerr-Newman black holes can support linear charged scalar fields in their exterior regions. These stationary massive charged scalar fields can form bound states, which are called stationary scalar clouds. In this paper, we show that Kerr-Sen black holes can also support stationary massive charged scalar clouds by matching the near- and far-region solutions of the radial part of the Klein-Gordon wave equation. We also review stationary scalar clouds within the background of static electrically charged black hole solutions in the low-energy limit of heterotic string field th…
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 minima…
We explore some (especially, thermodynamical) properties of the dyonic Kerr-Sen-AdS$_4$ black hole and its ultraspinning counterpart, and check whether or not both black holes satisfy the first law and Bekenstein-Smarr mass formulas. To this end, new Christodoulou-Ruffini-like squared-mass formulae for the usual dyonic Kerr-Sen-AdS$_4$ solution and its ultraspinning cousin are deduced. Similar to the ultraspinning Kerr-Sen-AdS$_4$ black hole case, we demonstrate that the ultraspinning dyonic Kerr-Sen-AdS$_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since th…
We investigate the weak cosmic censorship conjecture for Kerr-Sen black holes, which are solutions to the four-dimensional low-energy effective field theory for the heterotic string theory, based on the scattering of a charged scalar field. When the fluxes of the scalar field are assumed to transfer its conserved quantities to the black hole, extremal and near-extremal black holes cannot be over-spun and over-charged in their first-order variations, which is sufficient to conclude that the weak cosmic censorship conjecture is valid for Kerr-Sen black holes. We confirm our conclusion by relatin…
The dynamics of charged particles moving around a Kerr-Newman black hole surrounded by cloud strings, quintessence and electromagnetic field is integrable due to the presence of a fourth constant of motion like the Carter constant. The fourth motion constant and the axial-symmetry of the spacetime give a chance to the existence of radial effective potentials with stable circular orbits in two-dimensional planes, such as the equatorial plane and other nonequatorial planes. They also give a possibility of the presence of radial effective potentials with stable spherical orbits in the three-dimen…
We investigate the escape probabilities of the photons near the horizon of the Kerr-Sen black hole. We find that the escape probabilities of the photons are nonzero in the event horizon limit of the extreme Kerr-Sen black hole if the light sources are near the equator. We show that the escape probability of a photon increases with the radial position of the light source. It is also uncovered that the escape probability decreases if the light source with constant radius moves from the equatorial plane to the pole. Besides, we discover that the escape probability of a photon in the Carter frame …
Massive scalar test fields around Kerr black holes can form quasi-bound states with complex frequencies. Some of these states decay in time, but some others -- in the superradiant regime -- grow, causing a superradiant instability. Precisely at the threshold between decaying and growing modes, there exist bound states with real frequency, known as scalar clouds. Fully non-linear counterparts of these clouds have been shown to yield Kerr black holes with scalar hair. Here, we consider massive, (electrically) charged, test scalar and Proca fields on the background of Reissner-Nordström black hol…
It is reported that massive scalar fields can form bound states around Kerr black holes [C. Herdeiro, and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)]. These bound states are called scalar clouds, which have a real frequency $ω=mΩ_H$, where $m$ is the azimuthal index and $Ω_H$ is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition $ω=qΦ_H$ for the charged scalar field, where…
Motivated by advanced progress in the holographic theory between rotating black holes and CFT, we explore the conformal invariance on dyonic Kerr-Sen black hole and its gauged family. We consider a neutral massless scalar probe on the black holes' background within the low-frequency limit and exhibit that the solution space possesses $SL(2,R)\times SL(2,R)$ isometry. The periodic identification of the azimuthal angle corresponds to the spontaneous conformal symmetry breaking by temperatures $T_L,T_R$. Using the computation of the central charges on Ref. [25] that we recalculate by considering …
We investigate phase transitions and critical behaviors of the Kerr-Sen black hole in four dimensions. Computing the involved thermodynamical quantities including the specific heat and using the Ehrenfest scheme, we show that such a black hole undergoes a second-order phase transition. Adopting a new metric form derived from the Gibss free energy scaled by a conformal factor associated with extremal solutions, we calculate the geothermodynamical scalar curvature recovering similar phase transitions. Then, we obtain the scaling laws and the critical exponents, matching perfectly with mean field…
Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clo…
We argue about the (non) existence of {\it superregular} scalar clouds (i.e., bound states of a massive and complex-valued scalar field $Ψ$) around exact {\it extremal} ($a = M$) Kerr black holes (BH's) possessing {\it bounded radial derivatives at the horizon} (in Boyer-Lindquist coordinates) as opposed to similar cloud solutions that exist but with unbounded derivatives in the same coordinate system. The latter solutions have been reported recently both analytically and numerically. The superregular clouds cannot be obtained from the regular clouds around subextremal Kerr BH's ($|a|< M$) in …
We elaborate on basic properties of generalized Killing-Yano tensors which naturally extend Killing-Yano symmetry in the presence of skew-symmetric torsion. In particular, we discuss their relationship to Killing tensors and the separability of various field equations. We further demonstrate that the Kerr-Sen black hole spacetime of heterotic string theory, as well as its generalization to all dimensions, possesses a generalized closed conformal Killing-Yano 2-form with respect to a torsion identified with the 3-form occuring naturally in the theory. Such a 2-form is responsible for complete i…
A Kerr-Sen-like black hole solution appears in the Einstein-bumblebee theory of gravity. The solution contains contains a Lorentz violating parameter in an explicit manner. We study the null geodesics in the background of this Kerr-Sen-like black hole surrounded by a dispersive medium like plasma. We investigate the effect of the charge of the black hole, the Lorentz violation parameter, and the plasma parameter on the photon orbits with the evaluation of the effective potential in the presence of both the Lorentz violation parameter and the plasma parameter. We also study the influence of the…
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 …
We show that the integral method used to prove the no-hair theorem for Black Holes (BH's) in spherically symmetric and static spacetimes within the framework of general relativity with matter composed by a complex-valued scalar-field does not lead to a straightforward conclusion about the absence of hair in the stationary and rotating (axisymmetric) scenario. We argue that such a failure can be used to justify in a simple and heuristic way the existence of non-trivial boson clouds or hair found numerically by Herdeiro and Radu [1,2] and analytically by Hod in the test field limit [3-5]. This i…
Lorentz-Violating (LV) scenario gets involved through a bumblebee field vector field $B_μ$. A spontaneous symmetry breaking allows the field to acquires a vacuum expectation value that generates LV into the system. A Kerr-Sen-like solution has been found out starting from the generalized form of a radiating stationery axially symmetric black-hole metric. We compute the effective potential offered by the null geodesics in the bumblebee rotating black-hole spacetime. The shadow has been sketched for different variations of the parameters involved in the system. A careful investigation has been c…
An atom falling freely into a Kerr black hole in a Boulware-like vacuum is shown to emit radiation with a Planck spectrum at the Hawking temperature. For a cloud of falling atoms with random initial times, the radiation is thermal. The existence of this radiation is due to the acceleration of the vacuum field modes with respect to the falling atom. Its properties can be traced to the dominant role of conformal quantum mechanics (CQM) in the neighborhood of the event horizon. We display this effect for a scalar field, though the acceleration radiation has a universal conformal behavior that is …
The validity of the cosmic censorship conjecture for the Kerr-Sen black hole, which is a solution to the low-energy effective field theory for four-dimensional heterotic string theory, is investigated using charged particle absorption. When the black hole absorbs the particle, the charge on it changes owing to the conserved quantities of the particle. Changes in the black hole are constrained to the equation for the motion of the particle and are consistent with the laws of thermodynamics. Particle absorption increases the mass of the Kerr-Sen black hole to more than that of the absorbed charg…
The recently proved `no short hair' theorem asserts that, if a spherically-symmetric static black hole has hair, then this hair (the external fields) must extend beyond the null circular geodesic (the "photonsphere") of the corresponding black-hole spacetime: $r_{\text{field}}>r_{\text{null}}$. In this paper we provide compelling evidence that the bound can be {\it violated} by {\it non}-spherically symmetric hairy black-hole configurations. To that end, we analytically explore the physical properties of cloudy Kerr-Newman black-hole spacetimes -- charged rotating black holes which support lin…
The separated radial part of a massive complex scalar wave equation in the Kerr- Sen geometry is shown to satisfy the generalized spheroidal wave equation which is, in fact, a confluent Heun equation up to a multiplier. The Hawking evaporation of scalar particles in the Kerr-Sen black hole background is investigated by the Damour-Ruffini-Sannan method. It is shown that quantum thermal effect of the Kerr-Sen black hole has the same character as that of the Kerr-Newman black hole.
