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.
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.
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 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.
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…
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…
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…
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…
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…
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…
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 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.
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）
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.
We present the improved Mathematica code which computes quasinormal frequencies with the help of the Bernstein spectral method for a general class of black holes, allowing for asymptotically flat, de Sitter or anti-de Sitter asymptotic. The method is especially efficient when searching for purely imaginary and unstable modes and here it is used for detecting the instability region of a charged scalar field in the background of the charged asymptotically de Sitter dilatonic black hole. We show that the instability has superradiant nature and the dilaton field essentially influences the region o…
The rotating linear dilatonic black hole is an asymptotically non-flat solution to Einstein-Maxwell-Dilaton-Axion gravity theory due to the existence of non-trivial matter fields. We have analytically studied the wave equation of scalar field in this background and shown that the radial wave equation can be solved in terms of hypergeometric function. By determining the ingoing and the outgoing fluxes at the asymptotic infinity, we have found the analytical expressions for reflection coefficient and greybody factor for certain scalar modes. In the high frequency regime, we obtain the Hawking te…
Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a $9\%$ decrease in the damping rate and up to a $6\%$ decrease in the real oscillation frequency. However, the intensity of Hawking ra…
There has been some recent speculation that a connection may exist between the quasinormal-mode spectra of highly damped black holes and the fundamental theory of quantum gravity. This notion follows from a conjecture by Hod that the real part of the highly damped mode frequencies can be used to calibrate the semi-classical level spacing in the black hole quantum area spectrum. However, even if the level spacing can be fixed in this manner, it still remains unclear whether this implies a physically significant "duality" or merely a numerical coincidence. This tapestry of ideas serves as the mo…
Phase transitions and quasinormal modes of Euler-Heisenberg-dilaton AdS black holes
Jiangxi Normal University（江西师范大学）；Xihang University（西安大学）；Hunan Normal University（湖南师范大学）；Shaanxi University of Science and Technology（陕西科技大学）；Yangzhou University（扬州大学）
Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational $4d$ model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors $\vecλ_i$ obeying $\vecλ_i (\vecλ_1 + \vecλ_2) > 0$, $i =1,2$. The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. Th…
We address quasinormal modes of compact objects in several alternative theories of gravity. In particular, we focus on black holes and neutron stars with scalar hair. We consider black holes in dilaton-Einstein-Gauß-Bonnet theory, and in a generalized scalar-Einstein-Gauß-Bonnet theory. In the latter case scalarized black holes arise, and we study the stability of the different branches of solutions. In particular, we discuss how the spectrum of quasinormal modes is changed by the presence of a non-trivial scalar field outside the black hole horizon. We discuss the existence of an (effective) …
We study the scalar and vector channels of gravitational quasinormal modes for Lifshitz black branes emerging in Einstein-Maxwell-Dilaton and Einstein-Proca theories in four and five dimensions, finding significant differences between the two models. In particular, rather surprisingly, in the Einstein-Maxwell-Dilaton model the dispersion relations for the shear and sound modes are given by $ω_{shear} \sim -i\,k^4$ and $ω_{sound}\sim-i \,k^2$, while in the Einstein-Proca model they take the more conventional form $ω_{shear} \sim -i\,k^2$ and $ω_{sound}\sim k$, the proportionality constants depe…
Both scalar and Dirac quasinormal modes in Garfinkle-Horowitz-Strominger black hole spacetime are studied by using the WKB approximation and the Pöschl-Teller approximation. For scalar field, we find that the QNMs with higher dilatons decay more rapidly than that with lower ones. However, this is not the case for mass $m$. Fields with higher mass will decay more slowly. The similar behaviors appear in the case of Dirac field. We also find that QNM frequencies evaluated by using WKB approximation and Pöschl-Teller approximation have a good agreement with each other when mode number $n$ is small…
In this paper, we focus on the quantization of $4-$dimensional rotating linear dilaton black hole (RLDBH) spacetime describing an action, which emerges in the Einstein-Maxwell-Dilaton-Axion (EMDA) theory. RLDBH spacetime has a non-asymptotically flat (NAF) geometry. When the rotation parameter " $a$" vanishes, the spacetime reduces to its static form, the so-called linear dilaton black hole (LDBH) metric. Under scalar perturbations, we show that the radial equation reduces to a hypergeometric differential equation. Using the boundary conditions of the quasinormal modes (QNMs), we compute the a…
We investigate the quasinormal modes of a class of static and spherically symmetric black holes with the derivative coupling. The derivative coupling has rarely been paid attention to the study of black hole quasinormal modes. Specifically, we study the effect of derivative coupling on the quasinormal modes for four kinds of black holes. They are Reissner-Nordstrom black holes, Bardeen black holes, noncommunicative geometry inspired black holes and dilaton black holes. These black holes are not the solutions of vacuum Einstein equations which guarantees the effect of derivative coupling is not…
Charged black holes embedded in matter with anisotropic pressure: Horizon Structure and Quasinormal Mode Spectra
Illinois Center for Advanced Studies of the Universe, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校宇宙高级研究中心）；Center for AstroPhysical Surveys, National Center for Supercomputing Applications, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校国家超级计算应用中心天体物理调查中心）；Department of Astronomy, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校天文系）
Quasinormal mode (QNM) gravitational radiation from black holes is expected to be observed in a few years. A perturbative formula is derived for the shifts in both the real and the imaginary part of the QNM frequencies away from those of an idealized isolated black hole. The formulation provides a tool for understanding how the astrophysical environment surrounding a black hole, e.g., a massive accretion disk, affects the QNM spectrum of gravitational waves. We show, in a simple model, that the perturbed QNM spectrum can have interesting features.
In this thesis, Maggiore's method (MM), which evaluates the transition frequency that appears in the adiabatic invariant from the highly damped quasinormal mode frequencies (QNMFs), is used to investigate the entropy and area spectra of the Garfinkle-Horowitz-Strominger black hole (GHSBH), the four-dimensional Lifshitz black hole with zero dynamical exponent (ZZLBH), and the rotating linear dilaton black hole (RLDBH), respectively. For studying the GHSBH's quantization, instead of ordinary quasinormal modes (QNMs), the boxed QNMs (BQNMs) that are the characteristic resonance spectra of the con…
In this article, we study the stability of black hole solutions found in the context of dilatonic Horava-Lifshitz gravity in $1+1$ dimensions by means of the quasinormal modes approach. In order to find the corresponding quasinormal modes, we consider the perturbations of massive and massless scalar fields minimally coupled to gravity. In both cases, we found that the quasinormal modes have a discrete spectrum and are completely imaginary, which leads to damping modes. For a massive scalar field and a non-vanishing cosmological constant, our results suggest unstable behaviour for large values …
The recent birth of gravitational wave astronomy invites a new generation of precision tests of general relativity. Signatures of black hole (BH) mergers must be systematically explored in a wide spectrum of modified gravity theories. Here, we turn to one such theory in which the initial value problem for BH mergers is well posed, the Einstein-Maxwell-dilaton system. We present conservative estimates for the merger parameters (final spins, quasinormal modes) based on techniques that have worked well for ordinary gravity mergers and utilize information extracted from test particle motion in the…
We have studied the scalar perturbation of static charged dilaton black holes in 3+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 3+1 dimensions. The quasinormal modes for the scalar perturbations are calculated using the third order WKB method. The dilaton coupling constant has a considerable effect on the values of quasi normal modes. It is also observed that there is a linear relation between the quasi normal modes and the temperature for large black holes.
Generalizations of the Schwarzschild and Kerr black holes are discussed in an astrophysically viable generalized theory of gravity, which includes higher curvature corrections in the form of the Gauss-Bonnet term, coupled to a dilaton. The angular momentum of these black holes can slightly exceed the Kerr bound. The location and the orbital frequency of particles in their innermost stable circular orbits can deviate significantly from the respective Kerr values. Study of the quasinormal modes of the static black holes gives strong evidence that they are mode stable against polar and axial pert…
In the previous paper (Li, X. Z., Xi, P., Zhai, X. H.: Phys. Lett. B{\bf666}, 125-130 (2008)), we show the solutions of Einstein equations with static spherically-symmetric quintessence-like matter surrounding a global monopole. Furthermore, this monopole become a black hole with quintessence-like matter and a deficit solid angle when it is swallowed by an ordinary black hole. We study its quasinormal modes by WKB method in this paper. The numerical results show that both the real part of the quasinormal frequencies and the imaginary part decrease as the state parameter $w$, for scalar and gra…
