We compute the quasinormal frequencies for scalar perturbations of hairy black holes in four-dimensional Einstein-Maxwell-dilaton theory assuming a non-trivial scalar potential for the dilaton field. We investigate the impact on the spectrum of the angular degree, the overtone number, the charges of the black hole as well as the magnitude of the scalar potential. All modes are found to be stable. Our numerical results are summarized in tables, and for better visualization, we show them graphically as well.
Gravitational decoupling can add hair to the black holes by adding extra sources. The quasinormal modes of hairy black hole caused by gravitational decoupling for the massless scalar field, electromagnetic field, and gravitational perturbation are investigated. The equations of effective potential for three perturbations are derived in hairy black hole spacetime. We also study the time evolution corresponding to the three perturbations, and the quasinormal mode frequencies are calculated using the Prony method through the time-domain profiles. By analyzing the influence of the hairs ($α$, $l_0…
The quasinormal modes of charged and uncharged massive scalar fields and also of charged Dirac fields against the background of a charged spherical black hole endowed with a scalar hair have been investigated. Special emphasis has been given to the case where negative scalar charge dominates over the electric charge of the black hole which mimics an Einstein-Rosen bridge. Except for the complete monotonic behaviour of the damping (imaginary part of the quasinormal mode) against the charge of the black hole as opposed to the existence of a peak for the pure RN case, the qualitative behaviour do…
We sketch the results of calculations of the quasinormal frequencies of the electrically charged dilaton black hole. At the earlier phase of evaporation (Q is less than 0.7-0.8M), the dilaton black hole "rings" with the complex frequencies which differ negligibly from those of the Reissner-Nordstrom black hole. The spectrum of the frequencies weakly depends upon the dilaton coupling.
We exactly calculate the quasinormal frequencies of the electromagnetic and Klein-Gordon perturbations propagating in a five-dimensional dilatonic black hole. Furthermore we exactly find the quasinormal frequencies of the massive Dirac field. Using these results we study the linear stability of this black hole. We compare our results for the quasinormal frequencies and for the linear stability of the five-dimensional black hole with those already published.
We study charged fermionic perturbations in the background of two-dimensional charged Dilatonic black holes, and we present the exact Dirac quasinormal modes. Also, we study the stability of these black holes under charged fermionic perturbations.
We clarify the purely imaginary quasinormal frequencies of a massless scalar perturbation on the 3D charged-dilaton black holes. This case is quite interesting because the potential-step appears outside the event horizon similar to the case of the electromagnetic perturbations on the large Schwarzschild-AdS black holes. It turns out that the potential-step type provides the purely imaginary quasinormal frequencies, while the potential-barrier type gives the complex quasinormal modes.
The quantum spectra of area and entropy of higher dimensional linear dilaton black holes in various theories via the quasinormal modes method are studied. It is shown that quasinormal modes of these black holes can reveal themselves when a specific condition holds. Finally, we obtain that a higher dimensional linear dilaton black hole has equidistant area and entropy spectra, and both of them are independent on the spacetime dimension.
We calculate the quasinormal modes of static spherically symmetric dilatonic Reissner-Nordström black holes for general values of the electric charge and of the dilaton coupling constant. The spectrum of quasinormal modes is composed of five families of modes: polar and axial gravitational-led modes, polar and axial electromagnetic-led modes, and polar scalar-led modes. We make a quantitative analysis of the spectrum, revealing its dependence on the electric charge and on the dilaton coupling constant. For large electric charge and large dilaton coupling, strong deviations from the Reissner-No…
The analytic forms of the asymptotic quasinormal frequencies of a coupled scalar field in the Garfinkle-Horowitz-Strominger dilaton spacetime is investigated by using the monodromy technique proposed by Motl and Neitzke. It is found that the asymptotic quasinormal frequencies depend not only on the structure parameters of the background spacetime, but also on the coupling between the scalar fields and gravitational field. Moreover, our results show that only in the minimal couple case, i.e., $ξ$ tends zero, the real parts of the asymptotic quasinormal frequencies agrees with the Hod's conjectu…
We study neutral massless scalar field perturbations around an extreme dilaton black hole in 2 +1 dimensions: the wave equations of the massless scalar field is shown to be exactly solvable in terms of Whittaker functions. Thus, the quasinormal modes are computed exactly and shown to be purely imaginary: we show the existence of stable and unstable modes. Interestingly, the quasinormal modes do not depend on the black holes parameters and the fundamental mode is always unstable and depends only on the parameters of the test field. Also, we determine the quasinormal frequencies via the improved…
We study quasinormal modes of static Einstein-Gauss-Bonnet-dilaton black holes. Both axial and polar perturbations are considered and studied from $l=0$ to $l=3$. We emphasize the difference in the spectrum between the Schwarzschild solutions and dilatonic black holes. At large Gauss-Bonnet coupling constant a small secondary branch of black holes is present, when the dilaton coupling is sufficiently strong. The modes of the primary branch can differ from the Schwarzschild modes up to $10\%$. The secondary branch is unstable and possesses long-lived modes. We address the possible effects of th…
Einstein-Maxwell-dilaton theory is an interesting and well-motivated theoretical laboratory to explore the impact of new fundamental degrees of freedom in the context of testing the no-hair conjecture, due to the existence of hairy black hole solutions together with the propagation of scalar, vector and tensor modes. In this paper we compute the quasinormal mode spectrum of static and slowly rotating black holes for generic values of the dilaton coupling, within a weak electric charge approximation. Our results suggest that these spacetimes are stable for generic values of the dilaton coupling…
Perturbations of black holes with primary hair: time evolutions, quasinormal modes and greybody factors
CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学技术学院物理系CENTRA）
Numerical studies of the coupled Einstein-Klein-Gordon system have recently revealed that confined scalar fields generically collapse to form caged black holes. In the light of this finding, we analytically study the characteristic resonance spectra of the confined scalar fields in rotating linear dilaton black hole geometry. Confining mirrors (cage) are assumed to be placed in the near-horizon region of a caged rotating linear dilaton black hole $\frac{r_{m}-r_{2}}{r_{2}}\ll 1$ ($r_{m}$ is the radius of the cage and $r_{2}$ represents the event horizon). The radial part of the Klein-Gordon eq…
We construct a new class of asymptotically (a)dS black hole solutions of Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrodynamics. The obtained solutions possess a Coulomb electric charge, massive term and a non-abelian hair as well. We calculate the conserved and thermodynamic quantities, and investigate the validity of the first law of thermodynamics. Also, we investigate thermal stability conditions by using the sign of heat capacity through canonical ensemble. Next, we consider the cosmological constant as a thermodynamical pressure and study the van der…
Adopting the monodromy technique devised by Motl and Neitzke, we investigate analytically the asymptotic quasinormal frequencies of a coupled scalar field in the Gibbons-Maeda dilaton spacetime. We find that it is described by $ e^{βω}=-[1+2\cos{(\frac{\sqrt{2ξ+1}}{2} π)}]-e^{-β_I ω}[2+2\cos{(\frac{\sqrt{2ξ+1}}{2}π)}]$, which depends on the structure parameters of the background spacetime and on the coupling between the scalar and gravitational fields. As the parameters $ξ$ and $β_I$ tend to zero, the real parts of the asymptotic quasinormal frequencies becomes $T_H\ln{3}$, which is consistent…
Quasinormal Modes and Hawking Radiation of Black Holes with Primary Scalar Hair
Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava（奥帕瓦西里西亚大学物理研究所理论物理与天体物理研究中心）；Institute of Cosmology, Department of Physics and Astronomy, Tufts University（塔夫茨大学物理与天文学系宇宙学研究所）；Institute of Physics in Opava, Silesian University in Opava（奥帕瓦西里西亚大学奥帕瓦物理研究所）
We study the general spherical symmetric solutions of dilaton-modulus gravity non-minimally coupled to a Maxwell field, using methods from the theory of dynamical systems. We show that the solutions can be classified by the mass, the electric charge, and a third parameter which we argue can be related to a scalar charge. The global properties of the solutions are discussed.
It is well known that the charged scalar perturbations of the Reissner-Nordstrom metric will decay slower at very late times than the neutral ones, thereby dominating in the late time signal. We show that at the stage of quasinormal ringing, on the contrary, the neutral perturbations will decay slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly extreme RN black hole have the same imaginary parts (damping times) for charged and neutral perturbations. An explanation of this fact is not clear but, possibly, is connected with the Choptuik scaling.
We study the stability of black holes that are solutions of the dilaton gravity derived from string-theoretical models in two and five dimensions against to scalar field perturbations, using the Quasinormal Modes (QNMs) approach. In order to find the QNMs corresponding to a black hole geometry, we consider perturbations described by a massive scalar field non-minimally coupled to gravity. We find that the QNM's frequencies turn out to be pure imaginary leading to purely damped modes, that is in agreement with the literature of dilatonic black holes. Our result exhibits the unstable behavior of…
It has been recently found that for the near extremal Kerr black holes appearing of Zero Damped Modes (accompanied by qusinormal mode branching) signifies about inapplicability of the regime of small perturbations and the onset of turbulence. Here we show that this phenomena is not limited by Kerr or Kerr-Newman solutions only, but also takes place for rotating dilatonic black holes for which we have found Zero Damped Modes both numerically and analytically. We have also shown that, contrary to recent claims, there is no instability of a charged massive scalar field in the background of the ro…
The behavior of hairy black hole solutions, obtained by the gravitational decoupling (GD) method, is investigated under scalar perturbations. The quasinormal mode frequencies of such solutions are regulated by GD hair. The numerically generated wave solutions are derived for a range of values for the GD hairy black hole parameters, with higher-frequency modes very sensitive to them. The results are confronted with the corresponding ones for the Schwarzschild solution, whose deviations from it demonstrate a unique physical identification of GD hairy black holes. The method here presented compri…
We numerically calculate the quasinormal frequencies of the Klein-Gordon and Dirac fields propagating in a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory. For the Klein-Gordon field we use the Horowitz-Hubeny method and the asymptotic iteration method for second order differential equations. For the Dirac field we first exploit the Horowitz-Hubeny method. As a second method, instead of using the asymptotic iteration method for second order differential equations, we propose to take as a basis its formulation for coupled systems of first order differentia…
In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter "a", it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNMs in th…
The cosmic no hair conjecture is tested in the spherically symmetric Einstein-Maxwell-dilaton~(EMD) system with a positive cosmological constant $Λ$. Firstly, we analytically show that once gravitational collapse occurs in the massless dilaton case, the system of field equations breaks down inevitably in outer communicating regions or at the boundary provided that a future null infinity ${\cal I}^+$ exists. Next we find numerically the static black hole solutions in the massive dilaton case and investigate their properties for comparison with the massless case. It is shown that their Abbott-De…
We study the process of fully nonlinear dynamical scalarization starting from a charged black hole or a naked singularity in asymptotically flat spacetime in the Einstein-Maxwell-dilaton theory. Initially the dilaton field is negligible compared to the gravitational and the Maxwell field. Then the dilaton field experiences an immediate growth, later it oscillates with damping amplitude and finally settles down to a finite value. For a hairy black hole develops from an original Reissner-Nordström black hole, since the dilaton oscillation and decay are almost independent of the coupling paramete…
Dilaton black hole solutions in low energy string theory (well known as GMGHS black holes) have analogue black holes with a cosmological constant derived by Gao and Zhang. Here, we study quasi normal modes of this dilaton-de Sitter black hole under neutral scalar field perturbations. We have employed the sixth order WKB analysis to compute the quasi normal mode frequencies. A detailed study is done for the quasi normal mode frequencies by varying the parameters in the theory such as the mass, cosmological constant, dilaton charge and the spherical harmonic index. For the massive scalar field w…
Starting from the static, spherically symmetric black hole solutions in massless Einstein-Maxwell-dilaton (EMD) theories, we build a "skeleton" action, that is, we phenomenologically replace black holes by an appropriate effective point particle action, which is well suited to the formal treatment of the many-body problem in EMD theories. We find that, depending crucially on the value of their scalar cosmological environment, black holes can undergo steep "scalarization" transitions, inducing large deviations to the general relativistic two-body dynamics, as shown, for example, when computing …
Quasinormal modes of Dirac field in the background of a non-Schwarzschild black holes in theories with higher curvature corrections are investigated in this paper. With the help of the semi-analytic WKB approximation and further using of Padé approximants as prescribed in [1] we consider quasinormal modes of a test massless Dirac field in the Einstein-dilaton-Gauss-Bonnet (EdGB) and Einstein-Weyl (EW) theories. Even though the effective potential for one of the chiralities has a negative gap we show that the Dirac field is stable in both theories. We find the dependence of the modes on the new…
Chargeless massive scalar fields are studied in the spacetime of Born-Infeld dilaton black holes (BIDBHs). We first separate the massive covariant Klein-Gordon equation into radial and angular parts and obtain the exact solution of the radial equation in terms of the confluent Heun functions. Using the obtained radial solution, we show how one gets the exact quasinormal modes (QNMs) for some particular cases. We also solve the Klein-Gordon equation in the spacetime of BIDBH with a cosmic string in which we point out the effect of the conical deficit on the BIDBH. The analytical solutions of th…
We have studied the scalar perturbation of static charged dilaton black holes in 2+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2+1 dimensions. It is asymptotic to the anti-de Sitter space. The exact values of quasinormal modes for the scalar perturbations are calculated. For both the charged and uncharged cases, the quasinormal frequencies are pure-imaginary leading to purely damped modes for the perturbations.
We investigate the upper limit of the gravitational radiation released upon the collision of two dilatonic black holes by analyzing the Gauss-Bonnet term. Dilatonic black holes have a dilaton hair coupled with this term. Using the laws of thermodynamics, the upper limit of the radiation is obtained, which reflected the effects of the dilaton hair. The amount of radiation released is greater than that emitted by a Schwarzschild black hole due to the contribution from the dilaton hair. In the collision, most of the dilaton hair can be released through radiation, where the energy radiated by the …
We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordström black hole is observed.
We study two dimensional dilaton gravity and supergravity following hamiltonian methods. Firstly, we consider the structure of constraints of 2D dilaton gravity and then the 2D dilaton supergravity is obtained taking the squere root of the bosonic constraints. We integrate exactly the equations of motion in both cases and we show that the solutions of the equation of motion of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity only by boundary conditions on the fermionic variables, i.e. the black holes of 2D dilaton supergravity theory are exactly the same black holes of …
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）
In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $γ$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investig…
Exceptional Points in Quasinormal Spectra of Hairy Black Holes
College of Physics, Sichuan University（四川大学物理学院）；School of Data Science, Shanghai University of Finance and Economics Zhejiang College（上海财经大学浙江学院数据科学学院）
We study charged massless fermionic perturbations in the background of $4$-dimensional linear dilaton black holes in Einstein-Maxwell-dilaton theory with double Liouville-type potentials. We present the analytical fermionic quasinormal modes, whose Dirac equations are solved in terms of hypergeometric functions. We also discuss the stability of these black holes under the charged fermionic perturbations.
Holography relates the quasinormal modes frequencies of AdS black holes to the pole structure of the dual field theory propagator. These modes thus provide the timescale for the approach to thermal equilibrium in the CFT. Here, we study how such pole structure and, in particular, the time to equilibrium can get modified in the presence of a black hole hair. More precisely, we consider in AdS a set of relaxed boundary conditions that allow for a low decaying graviton mode near the boundary, which triggers an additional degree of freedom. We solve the scalar field response on such background ana…
A new numerical integration method for examining a black hole structure was realized. Black hole solutions with dilatonic hair of 4D low energy effective SuperString Theory action with Gauss-Bonnet quadratic curvature contribution were studied, using this method, inside and outside the event horizon. Thermodynamical properties of this solution were also studied.
We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential is fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuni…
