Massless Scalar Perturbations Research Articles

Phase Structure and Quasinormal Modes of AdS Black Holes in Rastall Theory

We discuss the P−V criticality and phase transition in the extended phase space of anti-de Sitter(AdS) black holes in four-dimensional Rastall theory and recover the Van der Waals (VdW) analogy of small/large black hole (SBH/LBH) phase transition when the parameters ωs and ψ satisfy some certain conditions. Later, we further explore the quasinormal modes (QNMs) of massless scalar perturbations to probe the SBH/LBH phase transition. It is found that it can be detected near the critical point, where the slopes of the QNM frequencies change drastically in small and large black holes.

Thermodynamic description and quasinormal modes of adS black holes in Born-lnfeld massive gravity with a non-abelian hair

We construct a new class of asymptotically (a)dS black hole solutions of Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrody­ namics. The obtained solutions possess a Coulomb electric charge, massive term and a non-abelian hair as well. We calculate the conserved and thermodynamic quantities, and investigate the validity of the first law of thermodynamics. Also, we investigate thermal stability conditions by using the sign of heat capacity through canonical ensemble. Next, we consider the cosmological constant as a thermodynamical pressure and study the van der Waals like phase transition of black holes in the extended phase space thermodynamics. Our results indicate the existence of a phase transition which is affected by the parameters of theory. Finally, we consider a massless scalar perturbation in the background of asymptotically adS solutions and calculate the quasinormal modes by employing the pseu­ dospectral method. The imaginary part of quasinormal frequencies is the time scale of a thermal state (in the conformal field theory) for the approach to thermal equilibrium.

The fastest relaxation rate of higher-dimensional Reissner–Nordström black hole

In the eikonal regime, we analytically calculate quasinormal resonance frequencies for massless scalar perturbations of the higher-dimensional Reissner–Nordström (RN) black holes. Remarkably, we find that the higher-dimensional RN black holes coupled with the massless scalar fields have the fastest relaxation rates in the Schwarzschild limit, this is qualitatively different from the four-dimensional case where the black hole with non-vanishing charge has the fastest relaxation rate.

Quasinormal modes and van der Waals-like phase transition of charged AdS black holes in Lorentz symmetry breaking massive gravity

Using the quasinormal modes of a massless scalar perturbation, we investigate the small/large black hole phase transition in the Lorentz symmetry breaking massive gravity. We mainly focus on two issues: (i) the sign change of slope of the quasinormal mode frequencies in the complex-[Formula: see text] diagram; (ii) the behaviors of the imaginary part of the quasinormal mode frequencies along the isobaric or isothermal processes. For the first issue, our result shows that, at low fixed temperature or pressure, the phase transition can be probed by the sign change of slope. While increasing the temperature or pressure to certain values near the critical point, there will appear the deflection point, which indicates that such method may not be appropriate to test the phase transition. In particular, the behavior of the quasinormal mode frequencies for the small and large black holes tend to be the same at the critical point. For the second issue, it is shown that the nonmonotonic behavior is observed only when the small/large black hole phase transition occurs. Therefore, this property can provide us with an additional method to probe the phase transition through the quasinormal modes.

Perturbing microscopic black holes inspired by noncommutativity

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel–Kramers–Brillouin (WKB) approximation we show that the widely used WKB method does not converge in the critical cases where instabilities show up at the third order. By employing the inverted potential method, we demonstrate that the instabilities are an artifact of the WKB method. Finally, we discuss the usefulness of the asymptotic iteration method to find the QNMs.

Strong Cosmic Censorship in higher-dimensional Reissner-Nordstr\xf6m-de Sitter spacetime

: It was recently shown that Strong Cosmic Censorship might be violated for near-extremally-charged black holes in 4-dimensional de Sitter space under scalar perturbations. Here, we extend the study of neutral massless scalar perturbations in higher dimensions and discuss the dimensional influence on the validity of Strong Cosmic Censorship hypothesis. By giving an elaborate description of neutral massless scalar perturbations of Reissner-Nordström-de Sitter black holes in d = 4, 5 and 6 dimensions we conclude that Strong Cosmic Censorship is violated near extremality.

Quasinormal Modes of the Schwarzschild Black Hole Surrounded by the Quintessence Field in Rastall Gravity**Supported by the National Nature Science Foundation of Education Department of Shannxi Province under Grant No. 15JK1077 and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No. BJ12-02

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 , 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 , 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 late time tails in an extreme Reissner–Nordström black hole: frequency domain analysis

In this paper, we revisit the study of the leading order late time decay tails of massless scalar perturbations outside an extreme Reissner–Nordström black hole. Previous authors have analysed this problem in the time domain; we analyse the problem in the frequency domain. We first consider initial perturbations with generic regular behaviour across the horizon on characteristic surfaces. For this set-up, we reproduce some of the previous results of Sela (2016 Phys. Rev. D 93 024054) using Fourier methods. Next we consider related initial data on hypersurfaces, and present decay results at timelike infinity, near future null infinity, and near the future horizon. Along the way, using the inversion symmetry of the extreme Reissner–Nordström spacetime, we relate the higher multipole Aretakis and Newman–Penrose constants for a massless scalar in this background.

Quasinormal modes of massless scalar fields for charged black holes in the Palatini-type gravity

The scrutiny of black hole perturbations and its application to testing gravity theories have been a very crucial frontier in modern physics. In this paper we study the quasi-normal modes (QNM) of massless scalar perturbations for various charged black holes in the Palatini-type theories of gravity. Specifically, we consider the Palatini $f(R)$ theory coupled with Born-Infeld nonlinear electrodynamics and the Eddington-inspired-Born-Infeld gravity (EiBI) coupled with Maxwell electromagnetic fields. Special attention is paid to Einstein-Born-Infeld black holes, EiBI charged black holes and Born-Infeld charged black holes within $R\pm R^2$ gravity. These charged black holes are shown to be stable and their quasi-normal frequencies, including the frequencies in the eikonal limit, are calculated by using the WKB method up to the 6th order. We compare the results with the Reissner-Nordstr\"om charged black hole and prove that both the changes in the gravity sector and the matter sector of the action alter the QNM spectra.

Phase Transition and Quasinormal Modes for Spherical Black Holes in 5D Gauss–Bonnet Gravity**Supported by the National Natural Science Foundation of China under Grant Nos 11647050, 11675139 and 51575420, and the Scientific Research Program Funded by Shaanxi Provincial Education Department under Grant No 16JK1394.

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.

Phase transition of charged-AdS black holes and quasinormal modes: A time domain analysis

In this work we use the quasinormal mode of a massless scalar perturbation to probe the phase transition of the charged-AdS black hole in time profile. The signature of the critical behavior of this black hole solution is detected in the isobaric process. This paper is a natural extension of [1, 2] to the time domain analysis. More precisely, our study shows a clear signal in term of the damping rate and the oscillation frequencies of the scalar field perturbation. We conclude that the quasinormal modes can be an efficient tool to detect the signature of thermodynamic phase transition in the isobaric process far from the critical temperature, but fail to disclose this signature at the critical temperature

Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity

In this work, we utilize the quasinormal modes (QNMs) of a massless scalar perturbation to probe the Van der Waals-like small and large black holes (SBH/LBH) phase transition of charged topological Anti-de Sitter (AdS) black holes in four-dimensional massive gravity. We find that the signature of this SBH/LBH phase transition is detected in the isobaric as well as in the isothermal process. This further supports the idea that the QNMs can be an efficient tool to investigate the thermodynamical phase transition.

Quasinormal modes and thermodynamics of linearly charged BTZ black holes in massive gravity in (anti) de Sitter space-time

In this work we study the Quasi-Normal Modes (QNMs) under massless scalar perturbations and the thermodynamics of linearly charged BTZ black holes in massive gravity in the (Anti)de Sitter ((A)dS) space-time. It is found that the behavior of QNMs changes with the massive parameter of the graviton and also with the charge of the black hole. The thermodynamics of such black holes in the (A)dS space-time is also analyzed in detail. The behavior of specific heat with temperature for such black holes gives an indication of a phase transition that depends on the massive parameter of the graviton and also on the charge of the black hole.

Behavior of quasinormal modes and high dimension RN–AdS black hole phase transition

In this work we use the quasinormal frequencies of a massless scalar perturbation to probe the phase transition of the high dimension charged-AdS black hole. The signature of the critical behavior of this black hole solution is detected in the isobaric as well as in isothermal process. This paper is a natural generalization of \cite{base} to higher dimensional spacetime. More precisely our study shows a clear signal for any dimension $d$ in the isobaric process. As to the isothermal case, we find out that this signature can be affected by other parameters like the pressure and the horizon radius. We conclude that the quasinormal modes can be an efficient tool to investigate the first order phase transition, but fail to disclose the signature of the second order phase transition.

Quasi normal modes and P-V criticallity for scalar perturbations in a class of dRGT massive gravity around black holes

We investigate black holes in a class of dRGT massive gravity for their quasi normal modes (QNMs) for neutral and charged ones using Improved Asymptotic Iteration Method (Improved AIM) and their thermodynamic behavior. The QNMs are studied for different values of the massive parameter m_g for both neutral and charged dRGT black holes under a massless scalar perturbation. As m_g increases, the magnitude of the quasi normal frequencies are found to be increasing. The results are also compared with the Schwarzchild de Sitter (SdS) case. P-V criticallity of the aforesaid black hoels under massles scalar perturbation in the de Sitter space are also studied in this paper. It is found that the thermodynamic behavior of a neutral black hole shows no physically feasible phase transition while a charged black hole shows a definite phase transition.

Quasinormal frequencies of self-dual black holes

One simplified black hole model constructed from a semiclassical analysis of loop quantum gravity (LQG) is called self-dual black hole. This black hole solution depends on a free dimensionless parameter P known as the polymeric parameter and also on the $a_{0}$ area related to the minimum area gap of LQG. In the limit of P and $a_{0}$ going to zero, the usual Schwarzschild-solution is recovered. Here we investigate the quasinormal modes (QNMs) of massless scalar perturbations in the self-dual black hole background. We compute the QN frequencies using the sixth order WKB approximation method and compare them with numerical solutions of the Regge-Wheeler equation. Our results show that as the parameter P grows, the real part of the QN frequencies suffers an initial increase and then starts to decrease while the magnitude of the imaginary one decreases for fixed area gap $a_{0}$. This particular feature means that the damping of scalar perturbations in the self-dual black hole spacetimes are slower, and their oscillations are faster or slower according to the value of P.

Signature of the Van der Waals like small-large charged AdS black hole phase transition in quasinormal modes

We calculate the quasinormal modes of massless scalar perturbations around small and large four-dimensional Reissner-Nordstrom-Anti de Sitter (RN-AdS) black holes. We find a dramatic change in the slopes of quasinormal frequencies in small and large black holes near the critical point where the Van der Waals like thermodynamic phase transition happens. This further supports that the quasinormal mode can be a dynamic probe of the thermodynamic phase transition.

Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole

We study the stability of extreme Reissner-Nordström-AdS black hole under massless scalar perturbations. We show that the perturbation on the horizon of the extreme Reissner-Nordström-AdS black hole experiences a power-law decay, instead of an exponential decay as observed in the nonextreme AdS black hole. On the horizon of the extreme Reissner-Nordström-AdS black hole, the blow up happens at lower order derivative of the scalar field compared with that of the extreme Reissner-Nordström black hole, which shows that extreme AdS black holes tend to instability in comparison to black holes in asymptotic flat space-times.

Quasinormal modes of a black hole in the deformed Hořava–Lifshitz gravity

We study the quasinormal modes of the massless scalar perturbation in the background of a deformed black hole in the Hořava–Lifshitz gravity with coupling constant λ=1. Our results show that the quasinormal frequencies depend on the parameter in the Hořava–Lifshitz gravity and the behavior of the quasinormal modes is different from those in the Reissner–Norström and Einstein–Born–Infeld black hole spacetimes. The absolute value of imaginary parts is smaller and the scalar perturbations decay more slowly in the deformed Hořava–Lifshitz black hole spacetime. This information can help us understand more about the Hořava–Lifshitz gravity.

Dynamical evolution of scalar perturbation in Hořava-Lifshitz black-hole spacetimes

We study the dynamical evolution of a massless scalar perturbation in the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz black-hole spacetimes with the coupling constants $\ensuremath{\lambda}=\frac{1}{3}$, $\ensuremath{\lambda}=\frac{1}{2}$ and $\ensuremath{\lambda}=3$, respectively. Our calculation shows that, for the three cases, the scalar perturbations decay without any oscillation in which the decay rate imprints the parameter of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz black hole. The results are quite different from those in the Schwarzschild AdS black hole and can help us understand more about the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity.