Massless Scalar Perturbations Research Articles

Quazinormal modes and greybody factor of black hole surrounded by a quintessence in the S-V-T modified gravity as well as shadow

The purpose of this study is to investigate the quasinormal modes (QNMs), greybody factors (GFs) and shadows in a plasma of a black hole (BH) surrounded by an exotic fluid of quintessence type in a scalar-vector-tensor modified gravity. The effects of a quintessence scalar field and the modified gravity (MOG) field on the QNM, GF, and shadow are examined. Using the sixth-order WKB approach, we investigate the QNMs of massless scalar and electromagnetic perturbations. Our findings show that as the quintessence and the MOG parameter (ϵ and α) increase, the oscillation frequencies decrease significantly. Gravitational wave damping, on the other hand, decreases with increasing ϵ and α. In addition, we obtain an analytical solution for the transmission coefficients (GF) and demonstrate that more thermal radiation reaches the observer at spatial infinity as both the ϵ and α parameters increase. We also investigate the effect of the plasma background on the BH shadow and show that as the plasma background parameter increases, the shadow radius slightly shrinks. Nevertheless, the shadow radius increases as α and ϵ increase. Particularly intriguing is the fact that increasing ϵ has a greater impact on the shadow radius than increasing α, indicating that the quintessence parameter has a greater impact than the MOG parameter.

Thermodynamics for regular black holes as intermediate thermodynamic states and quasinormal frequencies

The thermodynamics for regular black holes (RBHs) is considered under the restricted phase space (RPS) formalism. It is shown that the RPS formalism seems to hold for RBHs, however, in order for the extensive thermodynamic parameters to be independent from each other, the RBHs need to be viewed as intermediate thermodynamic states in a larger class of black holes (BHs) which admit both regular and singular states. This idea is checked for several classes of BHs. In particular, for the electrically charged Hayward class BHs, it is shown that the regular states can either be thermodynamically stable or unstable, depending on the amount of charges carried by the BHs. The quasinormal frequencies for the Hayward class BHs are also analyzed, and it turns out that, even for the thermodynamically unstable regular states, the dynamic stability still holds, at least under massless scalar perturbations.

Gravitational traces of bumblebee gravity in metric–affine formalism

This work explores various manifestations of bumblebee gravity within the metric–affine formalism. We investigate the impact of the Lorentz violation parameter, denoted as X, on the modification of the Hawking temperature. Our calculations reveal that as X increases, the values of the Hawking temperature attenuate. To examine the behavior of massless scalar perturbations, specifically the quasinormal modes, we employ the Wentzel–Kramers–Brillouin method. The transmission and reflection coefficients are determined through our calculations. The outcomes indicate that a stronger Lorentz–violating parameter results in slower damping oscillations of gravitational waves. To comprehend the influence of the quasinormal spectrum on time–dependent scattering phenomena, we present a detailed analysis of scalar perturbations in the time–domain solution. Additionally, we conduct an investigation on shadows, revealing that larger values of X correspond to larger shadow radii. Furthermore, we constrain the magnitude of the shadow radii using the EHT horizon–scale image of SgrA∗ . Finally, we calculate both the time delay and the deflection angle.

Deflection angle, quasinormal modes and optical properties of a de Sitter black hole in [formula omitted] ([formula omitted], [formula omitted]) gravity

The current study aims to examine the impact of the boundary term on the bending angle of light for a static spherically symmetric black hole in the modified gravity described by the f(T,B) function. To accomplish this objective, we employ the Ishihara et al. method, which enables us to compute the deflection angle of light for a receiver and source situated at finite distances from a lens object in a non-asymptotically flat spacetime. This method considers the receiver’s viewpoint, and the resulting deflection angle diverges as the distance from the lens object increases, owing to the non-asymptotically flat spacetime. Nevertheless, the divergence can be regulated by the boundary term parameter c0. For lower values of the parameter c0, the divergence can be minimized within the finite range of the observer and source. Furthermore, we calculate the quasinormal modes of massless scalar perturbations in the black hole’s background using the asymptotic iteration method (AIM) and Padé averaged sixth-order Wentzel–Kramers–Brillouin (WKB) approximation method. Our findings indicate that the real quasinormal modes and damping rates are significantly impacted by the model parameter c0. Subsequently, we investigate two optical characteristics of the black hole, namely the shadow and the emission rate. Our results show that with an increase in the boundary term parameter c0, both the shadow’s size and the evaporation rate decrease.

Probing regular MOG static spherically symmetric spacetime using greybody factors and quasinormal modes

We investigate the behavior of the regular modified gravity (MOG) static spherically symmetric black hole (BH) under massless scalar perturbation, gravitational perturbation, and massless Dirac perturbation. The dimensionless parameter left( alpha right) distinguishes this BH from a Schwarzschild BH. We derive the effective potential equations for three perturbations in the regular MOG BH. Using the derived potentials, we calculate the bounds of greybody factors (GFs). Next, we investigate the quasinormal mode (QNM) of the MOG BH by implementing the WKB method of sixth order. By analyzing the influence of the MOG parameter alpha for the BH we study on GF and QNM, we found that as alpha increases, the GFs increase proportionally. However, both gravitational wave oscillation frequency and damping decrease as alpha increases. Moreover, we examine the behavior of QNMs by considering how their frequency changes with the shape of potentials. As a result, we found that the frequency behavior is like the quantum mechanical one. The faster the wave decays, the larger the potential.

Exact conditions for quasi-normal modes of extremal M5-branes and exact WKB analysis

We study the quasi-normal modes (QNMs) of a massless scalar perturbation to the extremal M5-branes metric by using the exact WKB analysis. The exact WKB analysis provides two exact QNMs conditions depending on the argument of the complex frequency of the perturbation. The exact conditions show that the discontinuity of the perturbative part of the QNMs leads the non-perturbative part of themselves. We also find a new example of the Seiberg-Witten/gravity correspondence, which helps us to compute the QNMs from our conditions.

Entropy bound and EGUP correction of d-dimensional Reissner–Nordström black hole in rainbow gravity

Inspired by the pronounced effect of gravity’s Rainbow on black hole thermodynamics, entropy relations and bounds have been investigated for [Formula: see text]-dimensional Reissner–Nordström (RN) black hole in the framework of Rainbow gravity. Basic thermodynamic properties of the black hole have been derived for the event horizon and Cauchy horizon. Except for the horizon radius, they all crucially depend on the Rainbow functions. Bounds of the aforesaid thermodynamic quantities have been deduced for both horizons. Analyzing the specific heat capacity, stability conditions have been obtained. Also, the extremal phase of the black hole has been explored. Further, a comparative study has been carried out to distinguish between the effects of Rainbow gravity model parameters on the entropy bound by considering different Rainbow gravity functions. For massless scalar perturbation, quasinormal modes have been computed using modified WKB approach. We have investigated the quantum correction of the black hole in a Rainbow gravity background to obtain the effects of Extended Uncertainty Principle (EUP) and Generalized Uncertainty Principle (GUP) parameters. We have derived the Hawking temperature, specific heat, entropy and remnant masses of the black hole in the Extended General Uncertainty Principle (EGUP) framework, and with the help of graphical methods, we have compared our findings.

Echoes from braneworld wormholes

We have studied the stability of wormhole geometries, under massless scalar, electromagnetic and axial gravitational perturbations, in the context of higher dimensional spacetimes. Intriguingly, the construction of a wormhole spacetime in the presence of higher dimensions, known as braneworld wormholes, \emph{does not} require the existence of exotic matter fields, unlike the scenario in four spacetime dimensions. Being a nonvacuum spacetime, the effective potential experienced by the axial gravitational perturbation differs considerably from the scenarios involving black holes. In particular, the present work provides one of the first attempts to study the gravitational perturbations of the wormhole spacetimes. Our analysis, involving both analytical and numerical techniques, demonstrates that there are echoes in the time domain signal of all the perturbations and the echo time delay is intimately related to the parameters originating from higher dimensions. Thereby combining the attempt to search for wormholes and extra dimensions, with the existence of gravitational wave echoes. Implications and future directions have also been discussed.

Quasi-normal modes for the D3-branes and Exact WKB analysis

We demonstrate how the Exact WKB analysis works in the study of the quasi-normal modes (QNMs). We apply the Exact WKB analysis to a massless scalar perturbation to the D3-brane metric as a concrete example. The Exact WKB analysis provides an exact condition for the QNMs. We numerically check our exact condition by using the Borel-Padé approximation. We also present an analytic form and an asymptotic behavior of the QNMs.

Quasinormal oscillations and late-time tail of massless scalar perturbations of a magnetized black hole in Rastall gravity* *Supported by the National Natural Science Foundation of China (NNSFC) (11805166, 11925503, 12175076). We also gratefully acknowledge the financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro

In this study, we investigate the quasinormal mode and late-time tail of charged massless scalar perturbations of a black hole in generalized Rastall gravity. The black hole metric in question is spherically symmetric, accompanied by a power-Maxwell field surrounded by a quintessence fluid. We show that the massless scalar field, when dressed up with the magnetic field, acquires an effective mass, which significantly affects the properties of the resultant quasinormal oscillations and late-time tails. Specifically, the quasinormal frequencies become distorted and might even be unstable for particular spacetime configurations. Additionally, the exponent of the usual power-law tail is modified according to the modification in the structure of the branch cut of the retarded Green's function. In particular, as the effective mass is generated dynamically owing to the presence of the magnetic field, we may consider a process through which the field is gradually removed from the spacetime configuration. In this context, while the quasinormal oscillations converge to the case of massless perturbations, we argue that the properties of resultant late-time tails do not fall back to their massless counterpart. The relevant characteristics are investigated using numerical and analytic approaches.

Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors

In this paper, we discuss the effects of nonlinear electrodynamics (NED) on non-rotating black holes, parametrized by the field coupling parameter β and magnetic charge parameter P in detail. Particularly, we survey a large range of observables and physical properties of the magnetically charged black hole, including the thermodynamic properties, observational appearance, quasinormal modes and absorption cross sections. Initially, we show that the NED black hole is always surrounded by an event horizon and any magnetic charge is permissible. We then show that the black hole gets colder with increasing charge. Investigating the heat capacity, we see that the black hole is thermally stable between points of phase transition. Introducing a generalized uncertainty principle (GUP) with a quantum gravity parameter λ extends the range of the stable region, but the effect on temperature is negligible. Then we compute the deflection angle at the weak field limit, by the Gauss-Bonnet theorem and the geodesic equation, and find that even at the first order, the magnetic charge has a contribution due to the “field mass” term. Small changes of the charge contributes greatly to the paths of null geodesics due to the P 2 dependence of the horizon radius. Using a ray-tracing code, we simulate the observational appearance of a NED black hole under different emission profiles, thin disk and spherical accretion. We find that the parameter P has a very strong effect on the observed shadow radius, in agreement with the deflection angle calculations. We finally consider quasinormal modes under massless scalar perturbations of the black hole and the greybody factor. We find that the charge introduces a slight difference in the fundamental frequency of the emitted waveform. We find that the greybody factor of the NED black hole is strongly steepened by the introduction of increasing charge. To present observational constrains, we show that the magnetic charge of the M87* black hole is between 0 ≤ P ≤ 0.024 in units of M, in agreement with the idea that real astrophysical black holes are mostly neutral. We also find that LIGO/VIRGO and LISA could detect NED black hole perturbations from BHs with masses between 5 M ☉ and 8.0 · 108 M ☉. We finally show that for black holes with masses detected with LIGO so far, charged NED black holes would deviate from Schwarzschild by 5∼10 Hz in their fundamental frequencies.

Quasi-normal modes and microscopic description of 2D black holes

We investigate the possibility of using quasi-normal modes (QNMs) to probe the microscopic structure of two-dimensional (2D) anti-de Sitter (AdS2) dilatonic black holes. We first extend previous results on the QNMs spectrum, found for external massless scalar perturbations, to the case of massive scalar perturbations. We find that the quasi-normal frequencies are purely imaginary and scale linearly with the overtone number. Motivated by this and extending previous results regarding Schwarzschild black holes, we propose a microscopic description of the 2D black hole in terms of a coherent state of N massless particles quantized on a circle, with occupation numbers sharply peaked on the characteristic QNMs frequency hat{omega} . We further model the black hole as a statistical ensemble of N decoupled quantum oscillators of frequency hat{omega} . This allows us to recover the Bekenstein-Hawking (BH) entropy S of the hole as the leading contribution to the Gibbs entropy for the set of oscillators, in the high-temperature regime, and to show that S = N. Additionally, we find sub-leading logarithmic corrections to the BH entropy. We further corroborate this microscopic description by outlining a holographic correspondence between QNMs in the AdS2 bulk and the de Alfaro-Fubini-Furlan conformally invariant quantum mechanics. Our results strongly suggest that modelling a black hole as a coherent state of particles and as a statistical ensemble of decoupled harmonic oscillators is always a good approximation in the large black-hole mass, large overtone number limit.

Accurate quasinormal modes of the five-dimensional Schwarzschild-Tangherlini black holes

The objective of this paper is to construct the accurate (say, to 11 decimal places) frequencies of the quasinormal modes of the five-dimensional Schwarzschild-Tangherlini black hole using three major techniques: the Hill determinant method, the continued fractions method, and the WKB-Pad\'e method and to discuss the limitations of each. It is shown that for the massless scalar, gravitational tensor, gravitational vector, and electromagnetic vector perturbations considered in this paper, the Hill determinant method and the method of continued fractions (both with the convergence acceleration) always give identical results, whereas the WKB-Pad\'e method gives the results that are amazingly accurate in most cases. Notable exception are the gravitational vector perturbations ($j=2$ and $\ensuremath{\ell}=2$), for which the WKB-Pad\'e approach apparently does not work. Here we have an interesting situation in which the WKB-based methods (WKB-Pad\'e and WKB--Borel--Le Roy) give the complex frequency that differs from the result obtained within the framework of the continued fraction method and the Hill determinant method. For the fundamental mode, deviation of the real part of frequency from the exact value is 0.5% whereas the deviation of the imaginary part is 2.7%. For $\ensuremath{\ell}\ensuremath{\ge}3$ the accuracy of the WKB results is similar again to the accuracy obtained for other perturbations. The case of the gravitational scalar perturbations is briefly discussed.

Null geodesics and QNMs in the field of regular black holes

In this paper, we analyze the null geodesics of regular black holes (BHs). A detailed analysis of geodesic structure, both null geodesics and timelike geodesics, has been investigated for the said BH. As an application of null geodesics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the BH spacetime. Moreover, we determine the relation between radius of photon sphere [Formula: see text] and the shadow observed by a distance observer. Furthermore, we discuss the effect of various parameters on the radius of shadow [Formula: see text]. Also, we compute the angle of deflection for the photons as a physical application of null-circular geodesics. We find the relation between null geodesics and quasinormal mode (QNM) frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that (in the eikonal limit) the QNMs of BHs are governed by the parameter of null-circular geodesics. The real part of QNMs frequency determines the angular frequency, whereas the imaginary part determines the instability timescale of the circular orbit. Next, we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations are also discussed. As an application of timelike geodesics, we compute the innermost stable circular orbit (ISCO) and marginally bound circular orbit (MBCO) of the regular BHs which are closely related to the BH accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.

Stability analysis of a charged black hole with a nonlinear complex scalar field

It has been shown recently that the charged black hole can be scalarized if Maxwell field minimally couples with a complex scalar which has nonnegative nonlinear potential. We firstly prove that such scalarization cannot be a result of continuous phase transition for general scalar potential. Furthermore, we numerically find that it is possible that the RN black hole will be scalarized by a first order phase transition spontaneously and extreme RN black hole is not stable in micro-canonical ensemble. In addition, considering a massless scalar perturbation, we compute the quasi-normal modes of the scalarized charged black hole and the results imply that the spontaneously scalarized charged black hole is not only favored in thermodynamics but also is kinetically stable against scalar perturbation at linear level. Our numerical results also definitely gives negative answer to Penrose-Gibbons conjecture and two new versions of Penrose inequality in charged case are suggested.

Phase transition and quasinormal modes for charged black holes in 4D Einstein-Gauss-Bonnet gravity * *Supported by the National Natural Science Foundation of China (11605152, 11675139, 51802247) and Outstanding youth teacher programme from Yangzhou University

In four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, we consider the thermodynamic and phase transitions of (charged) AdS black holes. For the negative GB coefficient , the system allows two physical critical points, corresponding to the reentrant phase transition, when the charge . For arbitrary , the system always leads to a van der Waals phase transition. We then study the quasinormal modes (QNMs) of massless scalar perturbations to probe the van der Waals-like phase transition between small and large black holes (SBH/LBH) for (charged) AdS black holes. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNM frequencies change dramatically in small and large black holes near the critical point. The obtained results further support that QNMs can be a dynamic probe of thermodynamic properties in black holes.

Linear instability of charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet anti de-Sitter black holes * *Peng Liu is Supported by the Natural Science Foundation of China (11847055, 11905083). Chao Niu is Supported by the Natural Science Foundation of China (11805083). C. Y. Zhang is Supported by Natural Science Foundation of China (11947067, 12005077)

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.

Stability and quasinormal modes of black holes in conformal Weyl gravity

In this paper, we first investigate the thermal stability of black holes in conformal Weyl gravity with a comparison with the Schwarzschild black holes. Then, we consider a minimally coupled massive scalar perturbation and calculate the quasinormal modes in asymptotically dS spacetime by employing the sixth order WKB approximation and asymptotic iteration method. The deviations from those of the Schwarzschild-dS solutions are obtained and the possibility of the presence of quasi-resonance modes for Weyl black hole solutions is investigated. Finally, we consider a massless scalar perturbation in the background of asymptotically AdS solutions and calculate the quasinormal modes by using the pseudospectral method. The effects of the free parameter of the theory on the quasinormal modes are studied and deviations from those of the Schwarzschild-AdS black holes are investigated. The imaginary part of quasinormal frequencies in AdS spacetime is the time scale of a thermal state (in the conformal field theory) to approach thermal equilibrium.

Strong cosmic censorship for a scalar field in an Einstein-Maxwell-Gauss-Bonnet-de Sitter black hole * *This work is supported in part by NSFC (11005016, 11875196, 11375121)

It has been shown that the Christodoulou version of the strong cosmic censorship (SCC) conjecture can be violated for a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole. In this paper, we investigate the effects of higher derivative corrections to the Einstein-Hilbert action on the validity of SCC, by considering a neutral massless scalar perturbation in - and -dimensional Einstein-Maxwell-Gauss-Bonnet-de Sitter black holes. Our numerical results show that the higher derivative term plays a different role in the case than it does in the case. For , the SCC violation region increases as the strength of the higher derivative term increases. For , the SCC violation region first increases and then decreases as the higher derivative correction becomes stronger, and SCC can always be restored for a black hole with a fixed charge ratio when the higher derivative correction is strong enough. Finally, we find that the version of SCC is respected in the case, but can be violated in some near-extremal regimes in the case.

Instability and no-hair paradigm in d-dimensional charged-AdS black holes

Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed d-dimensional (d=4n+4 with conformal parameter n=0,1,2,...) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter n. It is also shown that the solutions presented here cannot be considered as scalar hairs for a Reissner-Nordstrom background. As a result, for d-dimensional small AdS black holes in the presence of a conformally invariant Maxwell source, the no-scalar hair paradigm seems to be supported.