Black holes in massive gravity: quasi-normal modes of scalar perturbations

We have studied quasinormal modes of scalar perturbations of a black hole in massive gravity. The parameters of the theory, such as the mass of the black hole, the scalar charge of the black hole and the spherical harmonic index is varied to see how the corresponding quasinormal frequencies change. We have also studied the massive scalar field perturbations. Most of the work is done using WKB approach while sections are devoted to compute quasinormal modes via the unstable null geodesics approach and the Pöschl–Teller approximation. Comparisons are done with the Schwarzschild black hole.     

Quasinormal Modes of Charged Dilaton Black Holes in 2 + 1 Dimensions

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.     

Fermionic quasinormal modes for two-dimensional Hořava–Lifshitz black holes

To obtain fermionic quasinormal modes, the Dirac equation for two types of black holes is investigated. It is shown that two different geometries lead to distinctive types of quasinormal modes, while the boundary conditions imposed on the solutions in both cases are identical. For the first type of black hole, the quasinormal modes have continuous spectrum with negative imaginary part that provides the stability of perturbations. For the second type of the black hole, the quasinormal modes have a discrete spectrum and are completely imaginary.     

Quasinormal Modes of the Planar Black Holes of a Particular Lovelock Theory

In this work, we study the scalar quasinormal modes of a planar black hole metric in asymptotic anti-de Sitter spacetime derived from a particular Lovelock theory. The quasinormal frequencies are evaluated by adopting the Horowitz-Hubeny method as well as a matrix formalism. Also, the temporal evolution of small perturbations is studied by using finite difference method. The roles of the dimension of the spacetime, the parameter of the metric k, as well as the temperature of the background black hole, are discussed. It is observed that the particular form of the metric leads to quasinormal frequencies whose real parts are numerically insignificant. The black hole metric is found to be stable against small scalar perturbations.     

On the Quasinormal Modes for Gravitational Perturbations of the Bardeen Black Hole

We investigate gravitational perturbations on a regular black hole described by the Bardeen solution. Bardeen’s black hole is a solution of Einstein’s equations with no singularity at the origin of the radially symmetric system. Notwithstanding this regularity, the Bardeen solution still has event horizons dependent on its characteristic parameters. When a black hole is perturbed, it oscillates and gives rise to damped vibrational modes known as quasinormal modes. Here, we compute the quasinormal frequencies of a regular black hole to third order in the WKB approximation for gravitational perturbations.     

Reissner-Nordstr?m de Sitte 黑洞的引力似正模

利用P?shl-Teller势近似方法,本文研究了径向和角向引力扰动引起的Reissner-Nordstr?m de Sitte 黑洞的似正模。研究表明,当宇宙常数增加时似正模虚部的强度变小,但它却随电荷、谐波数或轨道角动量增加而增加。当电荷固定而宇宙常数改变时,似正模的虚部与实部几乎成线性关系。研究还发现径向和角向引力扰动引起的似正模是一致的,这证实似正模只依赖于黑洞的参量而与初始扰动无关。     

Quasinormal modes of Reissner–Nördstrom black hole surrounded by quintessence

We evaluate the complex frequencies of the normal modes for the charged scalar field perturbations around a Reissner–Nördstrom black hole surrounded by a static and spherically symmetric quintessence using third order WKB approximation approach. Quintessence decreases the oscillation frequency and increases the damping time of quasinormal frequencies. We studied the variation of quasinormal frequencies with charge of the black bole, mass and charge of perturbing scalar field and the quintessential parameters.     

Quasinormal modes for tensor and vector type perturbation of Gauss Bonnet black hole using third order WKB approach

We obtain the quasinormal modes for tensor perturbations of Gauss–Bonnet (GB) black holes in d = 5, 7, 8 dimensions and vector perturbations in d = 5, 6, 7 and 8 dimensions using third order WKB formalism. The tensor perturbation for black holes in d = 6 is not considered because of the fact that the black hole is unstable to tensor mode perturbations. In the case of uncharged GB black hole, for both tensor and vector perturbations, the real part of the QN frequency increases as the Gauss–Bonnet coupling (α′) increases. The imaginary part first decreases upto a certain value of α′ and then increases with α′ for both tensor and vector perturbations. For larger values of α′, the QN frequencies for vector perturbation differs slightly from the QN frequencies for tensorial one. It has also been shown that as α′ → 0, the quasinormal frequencies for tensor and vector perturbations of the Schwarzschild black hole can be obtained. We have also calculated the quasinormal spectrum of the charged GB black hole for tensor perturbations. Here we have found that the real oscillation frequency increases, while the imaginary part of the frequency falls with the increase of the charge. We also show that the quasinormal frequencies for scalar field perturbations and the tensor gravitational perturbations do not match as was claimed in the literature. The difference in the result increases if we increase the GB coupling.     

Scalar Perturbations of Charged Dilaton Black Holes

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 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.     

A comparative study of Dirac quasinormal modes of charged black holes in higher dimensions

In this work we study the Dirac quasinormal modes of higher dimensional charged black holes. Higher dimensional Reissner–Nordström type black holes as well as charged black holes in Einstein–Gauss–Bonnet theories are studied for fermionic perturbations using WKB method. A comparative study of the quasinormal modes in the two different theories of gravity has been performed. The behavior of the frequencies with the variation of black hole parameters as well as with the variation of space-time dimensions is studied. We also study the large multipole number limit of the black hole potential in order to look for an analytic expression for the frequencies.     

Scalar and Dirac quasinormal modes of scalar-tensor-Gauss-Bonnet black holes

This study explores the scalar and Dirac quasinormal modes pertaining to a class of black hole solutions in the scalar-tensor-Gauss-Bonnet theory. The black hole metrics in question are novel analytic solutions recently derived in the extended version of the theory, which effectively follows at the level of the action of string theory. Owing to the existence of a nonlinear electromagnetic field, the black hole solution possesses a nonvanishing magnetic charge. In particular, the metric is capable of describing black holes with distinct characteristics by assuming different values of the ADM mass and the magnetic charge. This study investigates the scalar and Dirac perturbations in these black hole spacetimes; in particular, we focus on two different types of solutions, based on distinct horizon structures. The properties of the complex frequencies of the obtained dissipative oscillations are investigated, and the stability of the metric is subsequently addressed. We also elaborate on the possible implications of this study.     

Quasinormal Modes of Spherically Symmetric Curve Spacetime with Dark Matter Term

We study quasinormal modes of scalar field perturbation and electromagnetic field perturbation in a black hole space-time with dark matter by using WKB approximation method. The result shows clearly that the real part of black hole quasinormal modes is mainly determined by angular quantum number while its imaginary part mainly determined by model number. We also found out that the dark matter will restrain the perturbation frequency and slow down the speed of damping in spacetime. In addition; dark matter has a greater influence upon quasinormal modes in the electromagnetic field than that in the scalar field.     

Quasinormal Modes in Double-Charge de Sitter Black Hole

The black hole, as a hot topic to be regarded as a normally research to become a strong evidence for its existence, made more and more people get involved in its research. To calculating the quasinormal modes for massless scalar field and Maxwell’s field in double-charge de Sitter black hole by using WKB approximation method, there is a fact that the speed of weakening electromagnetic perturbation will be reduced. The quasinormal modes in black hole mainly depends on angular quantum number l when its real part is in lower-frequency circumstances. At the same time, imaginary part mainly depends on the overtone number n. When the black hole carries the same electronic quantity, the more the electronic charges have, the smaller the real part and imaginary part of quasinormal modes will be.     

Electromagnetic Quasinormal Modes in Hořava-Lifshitz Gravity

The electromagnetic quasinormal modes of Ho?ava-Lifshitz black hole is investigated by means of six-order WKB approach. We in this paper compare the quasinormal modes of this black hole with the charged black hole’s cases (we here take a regular charged black hole and Reissner-Nordström black hole for example). The numerical results of Ho?ava-Lifshitz’s quasinormal modes frequency show that the absolute value of imaginary part decrease as the parameter α increase. The fact means that charge in this spacetime make the quasinormal modes damp at a slower rate.     

Quasinormal Modes of Clifton–Barrow Black Holes

In this paper, we study the theoretical quasinormal modes produced by scalar perturbations around a static, spherically symmetric black hole with exterior metric described by the Clifton–Barrow solution of R ^1+δ gravity. It is found that the δ-correction increases both the real and imaginary part of the quasinormal frequency. Compared with those of ordinary Schwarzschild black hole with the same size, the oscillating quasi-period of scalar perturbation of Clifton–Barrow black hole is remarkably short for the case of low multi-pole quantum number l, while the difference of the damping time scales is slight. However, in the large l limit, the relative differences of both real and imaginary part of quasinormal modes have the same amplitude.     

Quasinormal Modes for Electromagnetic Field Perturbation of the Asymptotic Safe Black Hole

In this paper, the quasinormal modes (QNMs) of electromagnetic field perturbation to asymptotic safe (AS) black hole are discussed. Through six-order WKB approach we investigate the effects of quantum correction to the quasinormal modes (QNMs) numerically. Meanwhile by means of finite difference method, the evolutions of such perturbation to the safe black hole are figured out with corresponding parameters. It is found that the stability of black hole remains although the decay frequency and damping speed of oscillations are respectively increased and lowered by the quantum correction to classic Schwarzschild black hole.     

Quasinormal modes of non-Abelian hyperscaling violating Lifshitz black holes

We study the quasinormal modes of scalar field perturbations in the background of non-Abelian hyperscaling violating Lifshitz black holes. We find that the quasinormal frequencies have no real part so there is no oscillatory behavior in the perturbations, only exponential decay, that is, the system is always overdamped, which guarantees the mode stability of non-Abelian hyperscaling violating Lifshitz black holes. We determine analytically the quasinormal modes for massless scalar fields for a dynamical exponent \(z=2\) and hyperscaling violating exponent \(\tilde{\theta }>-2\). Also, we obtain numerically the quasinormal frequencies for different values of the dynamical exponent and the hyperscaling violating exponent by using the improved asymptotic iteration method.     

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 T_H\ln 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 a two-dimensional black hole

For a two-dimensional black hole we determine the quasinormal frequencies of the Klein–Gordon and Dirac fields. In contrast to the well known examples whose spectrum of quasinormal frequencies is discrete, for this black hole we find a continuous spectrum of quasinormal frequencies, but there are unstable quasinormal modes. In the framework of the Hod and Maggiore proposals we also discuss the consequences of these results on the form of the entropy spectrum for the two-dimensional black hole.     

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.