A large portion of the studies concerning the quasinormal mode frequencies of a Kerr black hole have focused only on achieving higher numerical accuracy with limited emphasis on providing their physical interpretation. In this article, we partially address this issue by computing the quasinormal mode frequency spectrum of a Kerr black hole using the theory of Regge poles. By considering the retarded Green's function of the Teukolsky equation, we establish for scalar, electromagnetic and gravitational perturbations an equation linking the Regge poles to the quasinormal frequencies and we solve it in the high-frequency regime to get "semiclassical" relations permitting us to obtain the complex frequencies of the weakly damped quasinormal modes from the Regge trajectories. Numerical results concerning gravitational perturbations ($s=-2$) are displayed. They are in excellent agreement with the "exact" ones in the eikonal regime $(\ell \gg 1)$ and in very good agreement even for lower values of $\ell$. Moreover, the splitting of each Regge pole of the Schwarzschild black hole into an infinite number of Kerr Regge poles explains the breaking of the azimuthal degeneracy of the quasinormal frequencies of the Schwarzschild black hole due to rotation. Our work is a first step to extend to Kerr black holes the approach developed for static spherically symmetric black holes which allowed, from a geometrical interpretation of the Regge poles in terms of the properties of the unstable circular null geodesics lying on the photon sphere, to derive accurate analytical formulas for the Regge trajectories and, as a by-product, for the complex frequencies of the weakly damped quasinormal modes.
We analytically calculate to leading order the asymptotic form of quasinormal frequencies of Kerr black holes in four, five and seven dimensions. All the relevant quantities can be explicitly expressed in terms of elliptical integrals. In four dimensions, we confirm the results obtained by Keshest and Hod by comparing the analytic results to the numerical ones.
The hidden Kerr/CFT proposal implies that the massless scalar wave equation in the near-region and low-frequency limit respects a hidden SL(2,R)$\times$SL(2,R) invariance in the Kerr black hole spacetime. We may use this symmetry to determine quasinormal frequencies (QNFs) of the massless scalar wave propagating around the Kerr black hole algebraically. It is shown that QNFs obtained using the hidden conformal symmetry near the horizon correspond approximately to not only those of scalar perturbation around the near-horizon region of a nearly extremal Kerr (NEK) black hole, but also those of n…
We develop the complex angular momentum method in the context of the BTZ black hole physics. This is achieved by extending a formalism introduced a long time ago by Arnold Sommerfeld, which allows us to define and use the Regge pole concept in a framework where the notion of an $S$ matrix does not exist. The Regge poles of the BTZ black hole are exactly obtained and from the associated Regge trajectories we determine its quasinormal mode complex frequencies. Furthermore, our approach permits us to physically interpret them: they appear as Breit-Wigner-type resonances generated by surface waves…
We consider a wide class of static spherically symmetric black holes of arbitrary dimension with a photon sphere (a hypersurface on which a massless particle can orbit the black hole on unstable circular null geodesics). This class includes various spacetimes of physical interest such as Schwarzschild, Schwarzschild-Tangherlini and Reissner-Nordström black holes, the canonical acoustic black hole or the Schwarzschild-de Sitter black hole. For this class of black holes, we provide general analytical expressions for the Regge poles of the $S$-matrix associated with a massless scalar field theory…
In the framework of the Lorentz symmetry breaking (LSB), we investigate the quasinormal modes (QNMs) and the greybody factors (GFs) of the Kerr-like black hole spacetime obtained from the bumblebee gravity model. In particular, we analyze the scalar and fermionic perturbations of the black hole within the framework of both semi-analytic WKB method and the time domain approach. The impacts of the LSB on the bosonic/fermionic QNMs and GFs of the Kerr-like black hole are investigated in detail. The obtained results are graphically depicted and discussed.
The quasinormal modes (QNMs) of a black hole spacetime are the free, decaying oscillations of the spacetime, and are well understood in the case of Kerr black holes. We discuss a method for computing the QNMs of spacetimes which are slightly deformed from Kerr. We mention two example applications: the parametric, turbulent instability of scalar fields on a background which includes a gravitational QNM, and the shifts to the QNM frequencies of Kerr when the black hole is weakly charged. This method may be of use in studies of black holes which are deformed by external fields or are solutions to…
In our recent study Ref. [1]: Eur. Phys. J. C 81, 501 (2021) , the main goal was to reveal the Lorentz symmetry breaking (LSB) effect in the rotating black holes via the greybody factor and quasinormal mode analyzes. Ding et al. [2] Kerr-like black hole solution of the bumblebee gravity model used in our paper [1] has unquestionably proven by Maluf and Muniz [3] that it is wrong. We now explain under which condition the greybody factor and quasinormal mode analyzes performed in [1] become valid. We re-make the calculations according to the condition in question and present the new results in t…
Quasinormal modes of scalar, electromagnetic, and gravitational fields in the extreme Schwarzschild-de Sitter background are known to be expressed in analytic form as eigenvalues of the Pöschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the Pöschl-Teller effective potential. Nevertheless, using the Frobenius method we find quasinormal modes analytically in this case as well. We write down the analytical formula for quasinormal frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is…
We compute the quasinormal mode frequencies and Regge poles of the canonical acoustic hole (a black hole analogue), using three methods. First, we show how damped oscillations arise by evolving generic perturbations in the time domain using a simple finite-difference scheme. We use our results to estimate the fundamental QN frequencies of the low multipolar modes $l=1, 2, \ldots$. Next, we apply an asymptotic method to obtain an expansion for the frequency in inverse powers of $l+1/2$ for low overtones. We test the expansion by comparing against our time-domain results, and (existing) WKB resu…
An analytic expression for the scalar quasinormal modes of the generic, spinning Kerr-$\mathrm{AdS_5}$ black holes was previously proposed by the authors in ref. 1, in terms of transcendental equations involving the Painlevé VI (PVI) $τ$ function. In this work, we carry out a numerical investigation of the modes for generic rotation parameters, comparing implementations of expansions for the PVI $τ$ function both in terms of conformal blocks (Nekrasov functions) and Fredholm determinants. We compare the results with standard numerical methods for the subcase of Schwarzschild black holes. We th…
We show that the linear perturbations of any spin field in the near-zone limit of the Kerr black hole are identical to those of an AdS$_2$ black hole which enjoys the same basic properties of the Kerr black hole. Thanks to this identification, we calculate the spectrum of the quasinormal modes and the Love numbers of Kerr black holes using an AdS$_2$/CFT$_1$ correspondence and a group theoretical approach.
We investigate quasinormal modes, greybody factor, and Hawking evaporation of a five-dimensional Kerr-anti de Sitter (AdS$_5$) black hole by solving a wave equation for a test massive scalar field in terms of the local Heun function. We clarify the distribution of the quasinormal modes satisfying the ingoing and decaying boundary conditions at the event horizon and conformal infinity, respectively, and their splitting behaviors in the complex frequency plane with respect to a variation of spin parameters. We also point out the existence of purely imaginary modes. Further, we develop a method t…
We show that nearly extremal Kerr black holes have two distinct sets of quasinormal modes, which we call zero-damping modes (ZDMs) and damped modes (DMs). The ZDMs exist for all harmonic indices $l$ and $m \ge 0$, and their frequencies cluster onto the real axis in the extremal limit. The DMs have nonzero damping for all black hole spins; they exist for all counterrotating modes ($m<0$) and for corotating modes with $0\leq μ\lesssim μ_c=0.74$ (in the eikonal limit), where $μ\equiv m/(l+1/2)$. When the two families coexist, ZDMs and DMs merge to form a single set of quasinormal modes as the bla…
We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal mode frequencies presented in a recent paper (arXiv:1212.3271). One set of modes, that we call "zero-damping modes", has vanishing imaginary part in the extremal limit, and exists for all corotating perturbations (i.e., modes with azimuthal index m being nonnegative). The other set (the "damped modes") retains a finite decay rate even for extremal Kerr black holes, and exists only for a subset of…
We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only a…
We compute numerically the quasinormal modes of Kerr-Newman black holes in the scalar case, for which the perturbation equations are separable. Then we study different approximations to decouple electromagnetic and gravitational perturbations of the Kerr-Newman metric, computing the corresponding quasinormal modes. Our results suggest that the Teukolsky-like equation derived by Dudley and Finley gives a good approximation to the dynamics of a rotating charged black hole for Q<M/2. Though insufficient to deal with Kerr-Newman based models of elementary particles, the Dudley-Finley equation shou…
In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies $ω$ and angular quantum numbers $λ$, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate as well as efficient method for investigating…
Using the Pöshl-Teller approximation, we evaluate the neutrino quasinormal modes (QNMs) of a Kerr-Newman-de Sitter black hole. The result shows that for a Kerr-Newman-de Sitter black hole, massless neutrino perturbation of large $Λ$, positive $m$ and small value of $n$ will decay slowly.
We study the spectrum of quasinormal mode frequencies for a Proca field on a rotating black hole spacetime. First, we review how the introduction of field mass modifies the spectrum in the scalar-field case, leading to evanescent modes and to quasiresonance. Next, we examine the three physical polarizations of the Proca field and their relation to the electromagnetic field modes in the massless limit. Exploiting a separation of variables, we obtain a five-term recurrence relation from an appropriate ansatz for the radial function. Gaussian elimination and the modified Lentz algorithm are appli…
We compute the quasinormal frequencies of rotating black holes using the continued fraction method first proposed by Leaver. The main difference with former works, is that our results are obtained by a new numerical technique which avoids the use of two dimensional root-finding routines. The technique is applied to evaluate the angular eigenvalues of Teukolsky's angular equation. This method allow us to calculate both the slowly and the rapidly damped quasinormal frequencies with excellent accuracy.
Quasinormal modes of a massive Dirac field were calculated for various static black hole backgrounds with the help of the WKB formula. These estimations, however, are rough and valid only for very small values of $μM$, where $M$ and $μ$ are mass of the black hole and field respectively. Thus, no accurate calculations of massive Dirac modes are known even for the Schwarzschild black hole and this is all the more so for the Kerr solution. Here we calculate quasinormal modes of a massive Dirac field in the Kerr background. We have shown that the infinitely long-lived quasinormal modes (quasireson…
We study analytically the quasinormal mode spectrum of near-extremal (rotating) Kerr black holes. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature T_{BH} and its horizon's angular velocity Ω, which is valid in the intermediate asymptotic regime 1<<ω<<1/T_{BH}.
In a recent paper (arXiv:1410.0694) Zilhão, Cardoso, Herdeiro, Lehner, and Sperhake have studied the nonlinear stability of Kerr-Newman black holes. We show that their numerical results for the time evolutions of the spacetime deformations of near-extremal Kerr-Newman black holes are described extremely well by a {\it universal} formula for the quasinormal resonances of the black holes. This formula is expressed in terms of the black-hole physical parameters: the horizon angular velocity $Ω_{\text{H}}$ and the Bekenstein-Hawking temperature $T_{\text{BH}}$.
We provide semi-analytic expressions for quasinormal mode frequencies of slowly rotating Kerr black holes to the quadratic order in the rotation parameter. We apply the parametrized black hole quasinormal mode ringdown formalism to the Chandrasekhar-Detweiler equation and the Sasaki-Nakamura equation instead of the Teukolsky equation, and compare our result with the previous numerical calculations.
We investigate the quasinormal modes for gravitational perturbations of rotating black holes in four dimensional Anti-de Sitter (AdS) spacetime. The study of the quasinormal frequencies related to these modes is relevant to the AdS/CFT correspondence. Although results have been obtained for Schwarzschild and Reissner-Nordstrom AdS black holes, quasinormal frequencies of Kerr-AdS black holes are computed for the first time. We solve the Teukolsky equations in AdS spacetime, providing a second order and a Pade approximation for the angular eigenvalues associated to the Teukolsky angular equation…
Using the WKB method, we show that the peak location ($r_{\rm peak}$) of the potential, which determines the quasinormal mode frequency of the Kerr black hole, obeys an accurate empirical relation as a function of the specific angular momentum $a$ and the gravitational mass $M$. If the quasinormal mode with $a/M \sim 1$ is observed by gravitational wave detectors, we can confirm the black-hole space-time around the event horizon, $r_{\rm peak}=r_+ +O(\sqrt{1-q})$ where $r_+$ is the event horizon radius. While if the quasinormal mode is different from that of general relativity, we are forced t…
In a study of the quasinormal mode frequencies of nearly extremal black holes, we pointed out a bifurcation of the mode spectrum into modes with finite decay and modes with vanishing decay in the extremal limit. We provided analytic and semi-analytic results identifying which families of modes bifurcated, and when modes with finite decay rates exist when approaching the extremal limit. In a recent note (arXiv:1510.05604), Hod suggests that additional modes asymptote to finite decay at extremely high spin parameter, based on past work by Detweiler. We search for these suggested modes and find n…
The resonant mode spectrum of the Kerr-Newman spacetime is presently unknown. These modes, called the quasinormal modes, play a central role in determining the stability of Kerr-Newman black holes and their response to perturbations. We present a new formalism, generalized from time-independent perturbation theory in quantum mechanics, for calculating the quasinormal mode frequencies of weakly charged Kerr-Newman spacetimes of arbitrary spin. Our method makes use of an original technique for applying perturbation theory to zeroth-order solutions that are not square- integrable, and it can be a…
We study analytically the fundamental resonances of near-extremal, slowly rotating Kerr-Newman black holes. We find a simple analytic expression for these black-hole quasinormal frequencies in terms of the black-hole physical parameters: omega=m Omega-2i pi T(l+1+n), where T and Omega are the temperature and angular velocity of the black hole. The mode parameters l and m are the spheroidal harmonic index and the azimuthal harmonic index of a co-rotating mode, respectively. This analytical formula is valid in the regime Im omega << Re omega <<1/M, where M is the black-hole mass.
We present a new method for determining the frequencies and wavefunctions of black hole quasinormal modes (QNMs) and Regge poles. The key idea is a novel ansatz for the wavefunction, which relates the high-$l$ wavefunctions to null geodesics which start at infinity and end in perpetual orbit on the photon sphere. Our ansatz leads naturally to the expansion of QNMs in inverse powers of angular momentum $L = l + 1/2$ (in 4D), and to the expansion of Regge poles in inverse powers of frequency. The expansions can be taken to high orders. We begin by applying the method to the Schwarzschild spaceti…
It is shown that the paper "Greybody radiation and quasinormal modes of Kerr-like black hole in Bumblebee gravity model", Eur. Phys. J. C 81, 501 (2021). arXiv:2102.06303, recently published in this journal is based on an incorrect result obtained by Ding et al., Eur. Phys. J. C 80, 178 (2020). arXiv:1910.02674, for a Kerr-like black hole solution.
The fundamental resonances of near-extremal Kerr black holes due to massive scalar perturbations are derived {\it analytically}. We show that there exists a critical mass parameter, $μ_c$, below which increasing the mass $μ$ of the field increases the oscillation frequency $\Re(ω)$ of the resonance. On the other hand, above the critical field mass increasing the mass $μ$ increases the damping rate $\Im(ω)$ of the mode. We confirm our analytical results by numerical computations.
We give an explicit expression for the frequencies of slowly damped quasinormal modes of near-extreme Kerr black holes. It follows from this expression that the near-extreme Kerr holes obey the Hod's bound: in the limit of maximal rotation, $\lim \sup ω_{IS}/T\leq π/ \hbar$, where $ω_{IS}$ is the decay rate of the slowest decaying quasinormal mode, $T$ is the black hole temperature. On the other hand, the bound is not saturated in the sense that $\lim \inf ω_{IS}/T< π/\hbar$ is a strict inequality. {\it It remains unclear} whether the bound is saturated in the sense that $\lim \sup ω_{IS}/T= π…
So far analysis of the quasinormal spectrum of a massive charged scalar field in the black hole background has been limited by the regime of small μM and qQ, where μ, q (M, Q) are mass and charge of the field (black hole). Here we shall present a comprehensive picture of quasinormal modes, late-time tails and stability of a massive charged scalar field around Kerr-Newman black holes for any physically meaningful values of the parameters. We shall show that despite presence of the two mechanisms of superradiance (owing to black hole's rotation and charge) and the massive term creating growing b…
By using the complex angular momentum approach, we prove that the quasinormal mode complex frequencies of the Schwarzschild black hole are Breit-Wigner type resonances generated by a family of surface waves propagating close to the unstable circular photon (graviton) orbit at $r=3M$. Furthermore, because each surface wave is associated with a given Regge pole of the $S$-matrix, we can construct the spectrum of the quasinormal-mode complex frequencies from Regge trajectories. The notion of surface wave orbiting around black holes thus appears as a fundamental concept which could be profitably i…
This note addresses quasinormal mode frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky's equations for Kerr-de Sitter black holes are mapped to Heun's equations, we are able to compute their quasinormal mode frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating bla…
Gravitational lensing in the weak field limit, quasinormal spectra, and gray-body factors are investigated in the Reissner-Nordström spacetime corrected by bounce parameters. Using the Gauss-Bonnet theorem, we analyze the effects of bounce corrections to the weak gravitational deflection angle and find that the divergence of the deflection angle can be suppressed by a bounce correction in the Reissner-Nordström spacetime. We also notice that the bounce correction plays the same role as the Morse potential in the deflection angle. Moreover, we derive the perturbation equations with the spin-dep…
Black-hole quasinormal modes (QNM) have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We compare numerical results for the QNM spectrum of the (rotating) Kerr black hole with an {\it exact} formula Re$ω\to T_{BH}\ln 3+Ωm$, which is based on Bohr's correspondence principle. We find a close agreement between the two. Possible implications of this result to the area spectrum of quantum black holes are discussed.
Motivated by the recent interest in quantization of black hole area spectrum, we consider the area spectrum of Kerr and extremal Kerr black holes. Based on the proposal by Bekenstein and others that the black hole area spectrum is discrete and equally spaced, we implement Kunstatter's method to derive the area spectrum for the Kerr and extremal Kerr black holes. The real part of the quasinormal frequencies of Kerr black hole used for this computation is of the form $mΩ$ where $Ω$ is the angular velocity of the black hole horizon. The resulting spectrum is discrete but not as expected uniformly…
The Dirac quasinormal modes (QNMs) of the Kerr-Newman black hole are investigated using continued fraction approach. It is shown that the quasinormal frequencies in the complex $ω$ plane move counterclockwise as the charge or angular momentum per unit mass of the black hole increases. They get a spiral-like shape, moving out of their Schwarzschild or Reissner-Nordström values and "looping in" towards some limiting frequencies as the charge and angular momentum per unit mass tend to their extremal values. The number of the spirals increases as the overtone number increases but decreases as the …
We compute for the first time very highly damped quasinormal modes of the (rotating) Kerr black hole. Our numerical technique is based on a decoupling of the radial and angular equations, performed using a large-frequency expansion for the angular separation constant_{s}A_{l m}. This allows us to go much further in overtone number than ever before. We find that the real part of the quasinormal frequencies approaches a non-zero constant value which does not depend on the spin s of the perturbing field and on the angular index l: ω_R=m\varpi(a). We numerically compute \varpi(a). Leading-order co…
We find quasinormal spectrum of the massive scalar field in the background of the Kerr black holes. We show that all found modes are damped under the quasinormal modes boundary conditions when $μM$ is not large, thereby implying stability of the massive scalar field. This complements the region of stability determined by the Beyer inequality for large masses of the field. We show that, similar to the case of a non-rotating black holes, the massive term of the scalar field does not contribute in the regime of high damping. Thereby, the high damping asymptotic should be the same as for the massl…
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…
The quasinormal resonant modes of massless neutral fields in near-extremal Kerr-Newman-de Sitter black-hole spacetimes are calculated in the eikonal regime. It is explicitly proved that, in the angular momentum regime ${\bar a}> \sqrt{{1-2{\barΛ}\over{4+{\barΛ}/3}}}$, the black-hole spacetimes are characterized by slowly decaying resonant modes which are described by the compact formula $\Imω(n)=κ_+\cdot(n+{1\over2})$ [here the physical parameters $\{{\bar a},κ_+,{\barΛ},n\}$ are respectively the dimensionless angular momentum of the black hole, its characteristic surface gravity, the dimensio…
The quasinormal frequencies of massive scalar fields on Kerr-AdS black holes are identified with poles of a certain meromorphic family of operators, once boundary conditions are specified at the conformal boundary. Consequently, the quasinormal frequencies form a discrete subset of the complex plane and the corresponding poles are of finite rank. This result holds for a broad class of elliptic boundary conditions, with no restrictions on the rotation speed of the black hole.
Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies
Institute for Cosmic Ray Research, The University of Tokyo（宇宙线研究所，东京大学）；Department of Physics, Tokyo Metropolitan University（物理学系，东京都立大学）；Yukawa Institute for Theoretical Physics, Kyoto University（汤川理论物理研究所，京都大学）
We present a method for determining the purely imaginary quasinormal modes of the Kerr geometry. Such modes have previously been explored, but we show that prior results are incorrect. The method we present, based on the theory of Heun polynomials, is very general and can be applied to a broad class of problems, making it potentially useful to all branches of physics. Furthermore, our application provides an example where the method of matched asymptotic expansions seems to have failed. A deeper understanding of why it fails in this case may provide useful insights for other situations.
This paper establishes the existence of quasinormal frequencies converging exponentially to the real axis for the Klein--Gordon equation on a Kerr-AdS spacetime when Dirichlet boundary conditions are imposed at the conformal boundary. The proof is adapted from results in Euclidean scattering about the existence of scattering poles generated by time-periodic approximate solutions to the wave equation.
We study {\it analytically} the asymptotic quasinormal spectrum of fermionic fields in the Kerr spacetime. We find an analytic expression for these black-hole resonances in terms of the black-hole physical parameters: its Bekenstein-Hawking temperature $T_{BH}$, and its horizon's angular velocity $Ω$, which is valid in the asymptotic limit $1 \ll ω_I \ll ω_R$. It is shown that according to Bohr's correspondence principle, the emission of a Rarita-Schwinger quantum ($s=3/2$) corresponds to a fundamental black-hole area change $ΔA=4\hbar \ln 2$, while the emission of a Weyl neutrino field ($s=1/…
The nonlinear superposition of the delta-metric and the Kerr metric results in delta-Kerr metric that represents a deformed Kerr black hole with delta = 1 + q, where q > 0 is proportional to the nonrelativistic quadrupole moment of the collapsed configuration. We study this spacetime and determine q_{+} such that for q, 0 < q < q_{+}, the outer spacetime singularity remains a null hypersurface. In this case, delta-Kerr spacetime represents a generalized black hole, namely, an asymptotically flat, stationary and axisymmetric vacuum solution of general relativity for which the outer singularity …
Quasinormal modes of Kerr-Newman-de Sitter black holes from Heun connection formulae
Toyota Technological Institute（丰田技术研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；Tokyo Metropolitan University（东京都立大学）；Nagoya University（名古屋大学）
The correspondence between the shadow radius and the quasi-normal modes of the Kerr-Sen black hole is studied. By using the equation of the shadow radius of the Kerr-Sen black hole and the angular separation constant of the quasi-normal modes, the expression of the real part of quasi-normal modes related to the shadow radius is obtained. We found that in the eikonal limit, our formula coincides with the previous result. Moreover, we also calculate the energy emission rate of the Kerr-Sen black hole, it turns out that the peak energy emissivity is inversely correlated with the charge parameter.
The quasinormal modes of Kerr-Newman black holes: a separated approach
Universidade de Lisboa – UL（里斯本大学）；National Technical University of Athens – Polytechnic Campus（雅典国立技术大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）；Pennsylvania State University（宾夕法尼亚州立大学）
The Sasaki-Nakamura transformation gives a short-ranged potential and a convergent source term for the master equation of perturbations in the Kerr space-time. In this paper, we study the asymptotic behavior of the transformation, and present a new relaxed necessary and sufficient condition of the transformation to obtain the short-ranged potential in the assumption that the transformation converges in the far distance. Also, we discuss quasinormal mode frequencies which are determined by the information around the peak of the potential in the WKB analysis. Finally, in the extreme Kerr limit, …
