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.     

Dirac quasinormal modes of Born-Infeld black hole spacetimes

Quasinormal modes (QNMs) for massless and massive Dirac perturbations of Born-Infeld black holes (BHs) in higher dimensions are investigated. Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated. We discuss the relationships between QNM frequencies and spacetime dimensions. Meanwhile, we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field. Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n. This shows that the Born-Infeld BHs become more and more unstable at higher dimensions. Furthermore, the traditional finite difference method is improved, so that it can be used to calculate the massive Dirac field. We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field. Because the number of extra dimensions is related to the string scale, there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.     

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.     

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.     

Hidden conformal symmetry of self-dual warped AdS<Subscript>3</Subscript> black holes in topological massive gravity

We extend the recently proposal of hidden conformal symmetry to the self-dual warped AdS₃ black holes in topological massive gravity. It is shown that the wave equation of massive scalar field with sufficient small angular momentum can be reproduced by the SL(2, R) Casimir quadratic operator. Due to the periodic identification in the φ direction, it is found that only the left section of hidden conformal symmetry is broken to U(1), while the right section is unbroken, which only gives the left temperature of dual CFT. As a check of the dual CFT conjecture of self-warped AdS₃ black hole, we further compute the Bekenstein–Hawking entropy and absorption cross section and quasinormal modes of scalar field perturbation and show these are just of the forms predicted by the dual CFT.     

Quasinormal modes in the background of charged Kaluza–Klein black hole with squashed horizons

We study the scalar perturbation in the background of the charged Kaluza–Klein black holes with squashed horizons. We find that the position of infinite discontinuities of the heat capacities can be reflected in quasinormal spectrum. This shows the possible non-trivial relation between the thermodynamical and dynamical properties of black holes.     

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.     

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.     

Quantum tunneling and quasinormal modes in the spacetime of the Alcubierre warp drive

In a seminal paper, Alcubierre showed that Einstein’s theory of general relativity appears to allow a super-luminal motion. In the present study, we use a recent eternal-warp-drive solution found by Alcubierre to study the effect of Hawking radiation upon an observer located within the warp drive in the framework of the quantum tunneling method. We find the same expression for the Hawking temperatures associated with the tunneling of both massive vector and scalar particles, and show this expression to be proportional to the velocity of the warp drive. On the other hand, since the discovery of gravitational waves, the quasinormal modes (QNMs) of black holes have also been extensively studied. With this purpose in mind, we perform a QNM analysis of massive scalar field perturbations in the background of the eternal-Alcubierre-warp-drive spacetime. Our analytical analysis shows that massive scalar perturbations lead to stable QNMs.     

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.     

Quasinormal Modes of Hayward Regular Black Hole

In this paper, using asymptotic iteration method and eikonal limit, the massive scalar quasinormal modes (QNM) is studied in regular Hayward spacetime, which is much similar to Schwarzschild black hole when r→∞ but there is no singularity at the center. We analyze the QNM frequencies ω by varying the parameter β (it is related to mass of black hole and cosmological constant), spherical harmonic index L and the mass of scalar field m. The results show that the effect of β could lead to the real part of ω increase but the imaginary part decrease, which imply that the existence of cosmological constant would impact on the process of a black hole relaxing after it has been perturbed.     

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.     

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.     

Greybody factors of charged dilaton black holes in 2 + 1 dimensions

We have studied the scalar perturbation of 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. The exact decay rates and the grey body factors for the massless minimally coupled scalar is computed for both the charged and the uncharged dilaton black holes. The charged and the uncharged black hole show similar behavior for grey body factors, reflection coefficients and decay rates.This revised version was published online in April 2005. The publishing date was inserted.     

Holographic superconductors in the AdS black-hole spacetime with a global monopole

We study holographic superconductors in the Schwarzschild–AdS black hole with a global monopole through a charged complex scalar field. We calculate the condensates of the charged operators in the dual conformal field theories (CFTs) and discuss the effects of the global monopole on the condensation formation. Moreover, we compute the electric conductive using the probe approximation and find that the properties of the conductive are quite similar to those in the Schwarzschild–AdS black hole. These results can help us know more about holographic superconductors in the asymptotic AdS black holes.     

Scalar field coupling to Einstein tensor in regular black hole spacetime

In this paper, we study the perturbation property of a scalar field coupling to Einstein’s tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant \(\eta \) imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein’s tensor in the regular black hole spacetimes by the 3rd order WKB method.     

Linear instability of charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet anti de-Sitter black holes

We study the linear instability of the charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet-AdS black holes by exploring their quasinormal modes.We find that the linear instability is triggered by superradiance.The charged massless scalar perturbation becomes more unstable with increasing Gauss-Bonnet coupling constant or black hole charge.Decreasing the AdS radius,on the other hand,will make the charged massless scalar perturbation more stable.The stable region in parameter space(α,Q,Λ)is given.Moreover,we find that the charged massless scalar perturbation is more unstable for larger scalar charge.The modes of multipoles are more stable than that of the monopole.     

Quasinormal modes of a Schwarzschild black hole immersed in an electromagnetic universe

We study the quasinormal modes(QNMs) of a Schwarzschild black hole immersed in an electromagnetic(EM) universe. The immersed Schwarzschild black hole(ISBH) originates from the metric of colliding EM waves with double polarization [Class. Quantum Grav. 12, 3013(1995)]. The perturbation equations of the scalar fields for the ISBH geometry are written in the form of separable equations. We show that these equations can be transformed to the confluent Heun's equations, for which we are able to use known techniques to perform analytical quasinormal(QNM) analysis of the solutions. Furthermore, we employ numerical methods(Mashhoon and 6~(th)-order Wentzel-Kramers-Brillouin(WKB)) to derive the QNMs. The results obtained are discussed and depicted with the appropriate plots.     

The entropy bound and the self-energy of charges in the Schwinger model on black hole backgrounds

We compute the q potential in the Schwinger model on the Schwarzschild black hole. This potential is also discussed using The WKB approximation by considering the rôle of zero modes of massive scalar fields. We study the entropy bound for a charged object using the generalized second law; and at the end, a scenario for charge confinement is proposed on AdS black holes.     

Absorption of fixed scalar in scattering off 4D N = 4 black holes

We perform the perturbation analysis of the black holes in the 4D, N = 4 supergravity. Analysis around the black holes reveals a complicated mixing between the dilation and other fields (metric and two U(1) Maxwell fields). It turns out that considering both s-wave (l = 0) and higher momentum modes (l ≠ 0), the dilaton as a fixed scalar is the only propagating mode when P = Q, h₁ = h₂ = 0 and F = −G = 2ϕ. We calculate the absorption cross-section for scattering of low frequency waves of fixed scalar and U(1) Maxwell fields off the extremal black hole.