Object Picture of Electromagnetic Quasinormal Ringing for a Stringy Black Hole

We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole.The objectpicture of the quasinormal ringing has been obtained by the finite difference method.Compared with a Schwarzschildblack hole,the results show that the electromagnetic field damps more slowly for a stringy black hole.

A Note on s-quasinormally Embedded and c-supplemented Subgroups of Finite Groups

In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.

BTZ Quasinormal Frequencies as Poles of Green’s Function

Based on the well known fact that the quasinormal frequencies are the poles of the frequency domain Green’s function we describe a method that allows us to calculate exactly the quasinormal frequencies of the Klein-Gordon field moving in the three-dimensional rotating Bañados-Teitelboim-Zanelli black hole. These quasinormal frequencies are already published and widely explored in several applications, but we use this example to expound the proposed method of computation. We think that the described procedure can be useful to calculate exactly the quasinormal frequencies of classical fields propagating in other backgrounds. Furthermore, we compare with previous results and discuss some related facts.

Asymptotic quasinormal modes of scalar field in a gravity's rainbow

In the framework of the gravity＇s rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically calculated the asymptotic quasinormal frequencies, which depend on not only the mass parameter of the black hole, but also the particle＇s energy of the perturbation field. Meanwhile, the real parts of the asymptotic quasinormal modes can be expressed as TH In 3, which is consistent with Hod＇s conjecture. In addition, for the quantum corrected black hole, the area spacing is independent of the particle＇s energy, even though the area itself depends on the particle＇s energy. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.

Quasinormal modes of the scalar field in five-dimensional Lovelock black hole spacetime

In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and oscillate more slowly in the Lovelock black hole background.

Dirac Quasinormal Modes of Reissner-Ndstrom Black Hole Surrounded by Quintessence

Using the third-order WKB approximation, we evaluate the quasinormal frequencies of massless Dirac field perturbation around a Reissner Nordstrom black hole surrounded by a static and spherically symmetric quintessence. We study the variation of quasinormal frequencies with the quintessential state parameter ε, the total angular momentum number ｜k｜, the charge Q, and the overtone number n changes, respectively. Moreover, from the results we obtained, we find that the massless Dirac field damps more slowly due to the presence of quintessence.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole: Gravitational, Electromagnetic and Massless Dirac Perturbations

In our previous work [Chin. Phys. Lett. 35（2018） 010410], the quasinormal modes of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel–Kramers–Brillouin approximative approach. In this study, we extend the work to the cases of gravitational, electromagnetic and massless Dirac perturbations. The result further confirms that the noncommutative parameter plays an important role for the quasinormal frequencies.

Quasinormal Modes of Phantom Scalar Perturbation in Background of Reissner-Nordstrom Black Hole

We have investigated the quasinormal modes （QNMs） of phantom scalar perturbation in a Reissner Nordstr6m （RN） background. We find that the dependence of Q, NMs on the mass of the field for the phantom perturbation is totally different from that of usual massive perturbation. However, we obtain the same critical value of the overtone number for an angular quantum number from which the mass will begin to have a reverse effect on the real part of QNM frequencies and the perturbation-independent relation between the Q, NMs and the second order thermodynamic phase transition.

Quasinormal modes of a stationary axisymmetric EMDA black hole

The massless scalar quasiaormal modes （QNMs） of a stationary axisymmetric Einstein-Maxwell dilato-axioa （EMDA） black hole are calculated numerically using the continued fraction method first proposed by Leaver. The fundamental quasinormal frequencies （slowly damped QNMs） are obtained and the peculiar behaviours of them are studied. It is shown that these frequencies depend on the dilaton parameter D, the rotational parameter a, the multiple moment l and the azimuthal number m, and have the same values with other authors at the Schwarzschild and Kerr limit.

Phase Transition and Quasinormal Modes for Spherical Black Holes in 5D Gauss–Bonnet Gravity

We study the quasinormal modes（QNMs） of massless scalar perturbations to probe the van der Waals like SBH/LBH phase transition of anti-de Sitter black holes in five-dimensional（5D） Gauss–Bonnet gravity. It is found that the signature of this SBH/LBH phase transition is detected when the slopes of the QNMs frequency change drastically and differently in small and large black holes near the critical point. The obtained results further support that the QNMs can be a dynamic probe to investigate the thermodynamic properties in black holes.

“Finite Groups with Quasinormal Subgroups of Prince Power Order”一文的一点注记

用F (G)代替F(G),将文"FiniteGroupswithQuasinormalSubgroupsofPrimePowerOrder,ActaMathHun gar89(4),2000,321-326"一文中的主要定理的可解性的假设去除,从而推广了该文的结论。

Jordanian Canonical Form of Quasinormal Operator

An operator on a Hilbert space is said to have (SI) decomposition if it is similar to the orthogonal direct sum of some (SI) operators. In this paper, we prove that every operator, which is similar to a quasinormal operator, has (SI)decomposition if and only if it is similar to D ( 0≤j<N λjS), where D is a diagonaloperator, λj is a positive number, N is a natural number or ∞, and S is the unilateral shift.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole

The quasinormal modes（QNMs） of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel-Kramers-Brillouin approximative approach. The result shows that the noncommutative parameter plays an important role for the quasinormal（QNM） frequencies.

Quasinormal modes and ringdown waveforms of a Frolov black hole

In this paper we investigate scalar perturbation over a Frolov black hole(BH), which is a regular BH induced by the quantum gravity effect. The quasinormal frequencies of a scalar field always consistently reside in the lower half-plane, and the time-domain evolution of the field demonstrates a decaying behavior, with the late-time tail exhibiting a power-law pattern. These observations collectively suggest the stability of a Frolov BH against scalar perturbation.Additionally, our study reveals that the quantum gravity effect leads to slower decay modes. For the case of the angular quantum number l = 0, the oscillation exhibits non-monotonic behavior with the quantum gravity parameter α_(0). However, once l ≥ 1, the angular quantum number surpasses the influence of the quantum gravity effect.

Quasinormal modes and isospectrality of Bardeen(Anti-)de Sitter black holes

Black holes(BHs)exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes(RBHs).The initial formulation of RBHs was presented by Bardeen,who considered the Einstein equation coupled with a nonlinear electromagnetic field.In this study,we investigate the gravitational perturbations,including the axial and polar sectors,of the Bardeen(Anti-)de Sitter black holes.We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes(QNMs)through numerical methods.For the Bardeen de Sitter black hole,we employ the 6thorder WKB approach.The numerical results reveal that the isospectrality is broken in this case.Conversely,the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.

Massless Dirac perturbations of black holes in f(Q)gravity:quasinormal modes and a weak deflection angle

This article considers a static and spherical black hole(BH)in f(Q)gravity.f(Q)gravity is the extension of symmetric teleparallel general relativity,where both curvature and torsion are vanishing and gravity is described by nonmetricity.In this study,we investigate the possible implications of quasinormal mode(QNM)modified Hawking spectra and deflection angles generated by the model.The Wentzel–Kramers–Brillouin method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter(Q_(0)).Based on the QNM computation,we can ensure that the BH is stable against massless Dirac perturbations and as Q_(0)increases the oscillatory frequency of the mode decreases.We then discuss the weak deflection angle in the weak field limit approximation.We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it.We find that the Q_(0)parameter reduces the deflection angle.

Probing the Bardeen-Kiselev black hole with the cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds

In this work,we investigate a static and spherically symmetric Bardeen-Kiselev black hole(BH)with the cosmological constant,which is a solution of the Einstein-non-linear Maxwell field equations.We compute the quasinormal frequencies for the Bardeen-Kiselev BH with the cosmological constant due to electromagnetic and gravitational perturbations.By varying the BH parameters,we discuss the behavior of both real and imaginary parts of the BH quasinormal frequencies and compare these frequencies with the Reissner-Nordström-de Sitter BH surrounded by quintessence(RN-dSQ).Interestingly,it is shown that the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ under electromagnetic perturbations are different when the charge parameter q,the state parameter w and the normalization factor c are varied;however,for the gravitational perturbations,the responses of the Bardeen-Kiselev BH with the cosmological constant and the RN-dSQ are different only when the charge parameter q is varied.Therefore,compared with the gravitational perturbations,the electromagnetic perturbations can be used to understand nonlinear and linear electromagnetic fields in curved spacetime separately.Another interesting observation is that,due to the presence of Kiselev quintessence,the electromagnetic perturbations around the Bardeen-Kiselev BH with the cosmological constant damps faster and oscillates slowly;for the gravitational perturbations,the quasinormal mode decays slowly and oscillates slowly.We also study the reflection and transmission coefficients along with the absorption cross section in the Bardeen-Kiselev BH with the cosmological constant;it is shown that the transmission coefficients will increase due to the presence of Kiselev quintessence.

The matrix method for black hole quasinormal modes

We provide a comprehensive survey of possible applications of the matrix method for black hole quasinormal modes. The proposed algorithm can generally be applied to various background metrics, and in particular, it accommodates both analytic and numerical forms of the tortoise coordinates, as well as black hole spacetimes. We give a detailed account of different types of black hole metrics, master equations, and the corresponding boundary conditions. Besides, we argue that the method can readily be applied to cases where the master equation is a system of coupled equations. By adjusting the number of interpolation points, the present method provides a desirable degree of precision, in reasonable balance with its efficiency. The method is flexible and can easily be adopted to various distinct physical scenarios.

Quasinormal Modes of the Schwarzschild Black Hole Surrounded by the Quintessence Field in Rastall Gravity

The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when η < 0, the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when η > 0, the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases.Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η,(l, n), ε and Nq, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.

On s-Quasinormal and c-Normal Subgroups of a Finite Group

Let F be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are shown： （1） G ∈ F if and only if there is a normal subgroup H such that G/H ∈ F and every maximal subgroup of all Sylow subgroups of H is either c-normal or s-quasinormally embedded in G; （2） G ∈F if and only if there is a soluble normal subgroup H such that G/H∈F and every maximal subgroup of all Sylow subgroups of F（H）, the Fitting subgroup of H, is either e-normally or s-quasinormally embedded in G.