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 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 of a stationary axisymmetric EMDA black hole

The massless scalar quasinormal modes (QNMs) of a stationary axisymmetric Einstein--Maxwell dilaton--axion (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.     

Gravitational perturbations of the Einstein-Euler-Heisenberg black hole

The prospect of using gravitational wave detections via the quasinormal modes (QNMs) to test modified gravity theories is exciting area of current research. Gravitational waves (GWs) emitted by a perturbed black hole (BH) will decay as a superposition of their QNMs of oscillations at the ringdown phase. In this work, we investigate the QNMs of the Einstein-Euler-Heisenberg (EEH) BH for both axial and polar gravitational perturbations. We obtain master equations with the tetrad formalism, and the quasinormal frequencies of the EEH BH are calculated in the 6th order Wentzel-Kramers-Brill?uin approximation. It is interesting to note that the QNMs of the EEH BH would differ from those of the Reissner-Nordstr?m BH under the EH parameter, which indicates the EH parameter would affect the gravitational perturbations for the EEH BH.     

Gravitational Perturbations in Einstein Aether Black Hole Spacetime

We study the gravitational perturbations in Einstein aether black hole spacetime and find that the quasinormal modes(QNMs) of the first kind of aether black hole are similar to that of a Lorentz violation(LV) model,the quantum electrodynamics(QED) extension limit of standard model extension. These similarities between completely different backgrounds may imply that LV in the gravity sector and LV in the matter sector have some connections: damping QNMs more rapidly and prolonging its oscillation period. Compared to the Schwarzschild case, the first kind of black holes have larger damping rates and the second ones have lower damping rates, and they all have smaller real oscillation frequency. These differences could be detected by the new generation of gravitational antennas.     

Massive Charged Quasinormal Modes of a Reissner-Nordström Black Hole

Using the WKB method and HYBRD program, we evaluate the low-lying massive charged scalar and Dirac field quasinormal modes (QNMs) of a Reissner-Nordström black hole. We discuss the real and imaginary parts of QNMs vary with the charge of black hole, the masses and charges of scalar and Dirac fields.     

Evolution of massive fields around a black hole in Hořava gravity

We study the evolution of massive scalar field in the spacetime geometry of Kehagias-Sfetsos black hole in deformed Hořava-Lifshitz (HL) gravity by numerical analysis. We find that the signature of HL theory is encoded in the quasinormal mode (QNM) phase of the evolution of field. The QNM phase in the evolution process lasts for a longer time in HL theory. QNMs involved in the evolution of massive field are calculated and find that they have a higher oscillation frequency and a lower damping rate than the Schwarzschild spacetime case. We also study the relaxation of field in the intermediate and asymptotic range and verified that behaviors of field in these phases are independent of the HL parameter and is identical to the Schwarzschild case.     

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.     

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 object picture of the quasinormal ringing has been obtained by the finite difference method. Compared with a Schwarzschild black hole, the results show that the electromagnetic field damps more slowly for a stringy black hole.     

Quasinormal Modes of Electromagnetic Perturbation around a Stringy Black Hole

We investigate the electromagnetic perturbation around a stringy black hole. A second-order differential equation is obtained for the perturbation. The variation of the effective potential with r is presented. The complex frequencies of the quasinormal modes of electromagnetic perturbation around a stringy black hole are computed by the third Wentzel-Kramers-Brillouin （WKB） approximation. The results show that the parameters resulted from the compactification of higher dimensions can influence the quasinormal complex frequencies, and the Maxwell field around a stringy black hole damps more slowly than that around a Schwarzschild black hole.     

Area spectra of near extremal black holes

Motivated by Maggiore’s new interpretation of quasinormal modes, we investigate area spectra of a near extremal Schwarzschild–de Sitter black hole and a higher-dimensional near extremal Reissner–Nordstrom–de Sitter black hole. The result shows that the area spectra are equally spaced and irrelevant to the parameters of the black holes.     

Periodicity and area spectrum of black holes

The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon areas of a Schwarzschild black hole and a Kerr black hole. It is shown that the equally spaced area spectrum for both cases takes the same form and the spacing is the same as that obtained through the quasinormal mode frequencies. Particularly, for a Kerr black hole, the small angular momentum assumption, which is necessary from the perspective of quasinormal mode, is not employed as the general area spacing is reproduced.     

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.     

Dynamical Evolution of a Scalar Field Coupling to Einstein’s Tensor in Charged Braneworld Black Holes

In this work, we study the quasinormal modes (QNMs) of scalar field coupling to Einstein’s tensor in charged braneworld black hole. The shape of the potential function is illustrated and we find that lower coupling constant leads to more stable field. We then apply six-order WKB approximation to calculate the quasinormal frequencies (QNF) in weaker coupling field, and depict the dependence of the oscillation frequency on the coupling constant. Furthermore, we use finite difference method to shape the evolution of the coupling field and find that coupling field with lower multipole numbers l corresponds to stable field, while higher l tends to lead to instability when the coupling constant is larger than a threshold value. Finally the fitting curve of such threshold value is given numerically.     

Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.     

Electromagnetic quasinormal modes of D-dimensional black holes II

By using the sixth order WKB approximation we calculate for an electromagnetic field propagating in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes its quasinormal (QN) frequencies for the fundamental mode and first overtones. We study the dependence of these QN frequencies on the value of the cosmological constant and the spacetime dimension. We also compare with the results for the gravitational perturbations propagating in the same background. Moreover we compute exactly the QN frequencies of the electromagnetic field propagating in D-dimensional massless topological black hole and for the charged D-dimensional Nariai spacetime we calculate exactly the QN frequencies of the coupled electromagnetic and gravitational perturbations.     

The ringing of quantum corrected Schwarzschild black hole with GUP

Schwarzschild black holes with quantum corrections are studied under scalar field perturbations and electromagnetic field perturbations to analyze the effect of the correction term on the potential function and quasinormal mode (QNM). In classical general relativity, spacetime is continuous and there is no existence of the so-called minimal length. The introduction of the correction items of the generalized uncertainty principle, the parameter β, can change the singularity structure of the black hole gauge and may lead to discretization in time and space. We apply the sixth-order WKB method to approximate the QNM of Schwarzschild black holes with quantum corrections and perform numerical analysis to derive the results of the method. Also, we find that the effective potential and QNM in scalar fields are larger than those in electromagnetic fields.     

Wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole

Using Leaver's continue fraction and time domain method, we investigate the wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole. We find that the presence of the negative kinetic energy terms modifies the standard results in quasinormal spectrums and late-time behaviors of the scalar perturbations. The phantom scalar perturbation in the late-time evolution will grow with an exponential rate.     

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.     

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.