Black hole (BH) solution in the conformal Weyl gravity is a generalization of the Schwarzschild spacetime which includes two additional constants appearing when integrating the third order differential equations for gravitational field. One constant looks like the effective cosmological constant providing the de Sitter asymptotic of the solution. The other constant allows one to describe flat rotation of galaxies without introducing of the dark matter. Here we show that the effective "dark matter" term in the metric function drastically changes the asymptotic behavior of the evolution of the wave function of a scalar field: after the Schwarzschild-like ringing phase, the ringing at another, non-Schwarzschildian, longer-lived frequency takes place before the beginning of the exponential asymptotic tail. Thus the evolution of the scalar field consists of the three qualitatively different stages: the Schwarzschild-like ringing phase, the effective dark matter ringing phase and the de Sitter phase characterized by exponential tails. The late time behavior of the electromagnetic field is qualitatively different as well: the exponential tails appear even in the absence of the effective de Sitter term.
Modelling of gravitational waves from binary black hole inspiral has played an important role in the recent observations of such signals. The late-stage ringdown phase of the gravitational waveform is often associated with the null particle orbit ("light ring") of the black hole spacetime. With simple models we show that this link between the light ring and spacetime ringing is based more on the history of specific models than on an actual constraining relationship. We also show, in particular, that a better understanding of the dissociation of the two may be relevant to the astrophysically in…
Recently, Cardoso et al. [arXiv:2109.00005] found an exact solution describing the black hole immersed in a galactic-like distribution of matter. There, the properties of gravitational radiation were studied. Here we continue analysis of properties of this geometry via consideration of the electromagnetic radiation. We calculate quasinormal modes, asymptotic tails and grey-body factors for electromagnetic radiation. In addition, we discuss the Unruh temperature for this spacetime. Estimations made in the regime which is best fitting the galaxies behavior show that influence of the environment …
The gravitational consequence of local Lorentz violation (LV) should show itself in derivation of the characteristic quasinormal ringing of black hole mergers from their general relativity case. In this paper, we study quasinormal modes (QNMs) of the scalar and electromagnetic field perturbations to Einstein aether black holes. We find that quasinormal ringing of the first kind aether black hole is similar to that of another Lorentz violation model---the QED-extension limit of standard model extension. These similarities between completely different backgrounds may imply that LV in gravity sec…
The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green's function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode excitation for Kerr black holes. Relying on the formalism developed by Mano, Suzuki and Takasugi, we improve and extend previous calculations of the quasinormal mode residues in the complex frequency plane ("excitation factors" B_q). Using these results we compute the "excitation coefficients" C_q (essentially the mode amplitudes) in the special case where the s…
We compute characteristic (quasinormal) frequencies corresponding to decay of a massive charged scalar field in a Reissner-Nordstrom black hole background. It proves that, contrary to the behavior at very late times, at the stage of quasinormal ringing the neutral perturbations will damp slower than the charged ones. In the limit of the extremal black hole the damping rate of charged and neutral perturbations coincides. Possible connection of this with the critical collapse in a massive scalar electrodynamics is discussed.
Quasinormal ringing of acoustic black holes in Laval nozzles is discussed. The equation for sounds in a transonic flow is written into a Schrödinger-type equation with a potential barrier, and the quasinormal frequencies are calculated semianalytically. From the results of numerical simulations, it is shown that the quasinormal modes are actually excited when the transonic flow is formed or slightly perturbed, as well as in the real black hole case. In an actual experiment, however, the purely-outgoing boundary condition will not be satisfied at late times due to the wave reflection at the end…
We investigate a condensed matter ``black hole'' analogue, taking the Gross-Pitaevskii (GP) equation as a starting point. The linearized GP equation corresponds to a wave equation on a black hole background, giving quasinormal modes under some appropriate conditions. We suggest that we can know the detailed characters and corresponding geometrical information about the acoustic black hole by observing quasinormal ringdown waves in the low temperature condensed matters.
A simple one-parameter generalization of the Schwarzschild spacetime was recently suggested by A. Simpson and M. Visser [JCAP 1902, 042 (2019)] as a toy model describing the regular black hole and traversable wormhole states separated by the border (one-way wormhole) state. We study quasinormal modes of all the three states and show that the black-hole/wormhole transition is characterized by echoes, while the remnant of the black hole state is kept in the time-domain profile of the wormhole perturbation at the initial stage of the exponential fall off. Calculations of quasinormal modes using t…
The general parametrization of spherically symmetric and asymptotically flat black-hole spacetimes in arbitrary metric theories of gravity was suggested in [3]. The parametrization is based on the continued fraction expansion in terms of the compact radial coordinate and has superior convergence and strict hierarchy of parameters. It is known that some observable quantities, related to particle motion around the black hole, such as the eikonal quasinormal modes, radius of the shadow, frequency at the innermost stable circular orbit, and others, depend mostly on only a few of the lowest coeffic…
Asymptotically safe gravity is based on the idea that the main contribution to the Schwarzschild-like black hole spacetime is due to the value of the gravitational coupling which depends on the distance from the origin and approaches its classical value in the far zone. However, at some stage this approach has an arbitrariness of choice of some identification parameter. The two cases of identification are considered here: first, by the modified proper length (the Bonanno-Reuter metric), and second, by the Kretschmann scalar (the metric for this case coincides, up to the redefinition of constan…
From information theory and thermodynamic considerations a universal bound on the relaxation time $τ$ of a perturbed system is inferred, $τ\geq \hbar/πT$, where $T$ is the system's temperature. We prove that black holes comply with the bound; in fact they actually {\it saturate} it. Thus, when judged by their relaxation properties, black holes are the most extreme objects in nature, having the maximum relaxation rate which is allowed by quantum theory.
While the linear behavior of gravity in braneworld models is well understood, much less is known about full non-linear gravitational effects. Even when they agree at the linear level, these could be expected to distinguish braneworlds from a lower-dimensional theory with no brane. Black holes are a good testing ground for such studies, as they are nonlinear solutions that would be expected to reflect the background geometry. In particular, we assess the role of black hole quasinormal modes in gravitational experiments devised to be sensitive to the existence of the brane, in a lower-dimensiona…
The gravitational radiation produced by binary black holes during their inspiral, merger, and ringdown phases is a promising candidate for detection by the first or second generation of kilometer-scale interferometric gravitational wave antennas. Waveforms for the last phase, the quasinormal ringing, are well understood. I discuss the feasibility of detection of the quasinormal ringing of a black hole based on an analysis of the Caltech 40-meter interferometer data.
In the scope of black hole spectroscopy, several attempts have been made in the past decades in order to test black holes or gravitational theories via black hole quasinormal modes. In the eikonal approximation, the quasinormal modes are generically associated with the photon ring of the black hole. This correspondence is valid for most cases in general relativity, but may not be true in other theories of gravity. In this paper, we consider the generalized energy-momentum squared gravity in which matter fields are non-minimally coupled to geometry. We investigate the axial perturbations of the…
We study gravitational perturbations of slowly-rotating black holes in a general effective-field-theory extension of general relativity that includes up to eight-derivative terms. We show that two Schrödinger-like equations with spin-dependent effective potentials govern the odd - and even-parity master variables. These equations are coupled for parity-violating corrections, and this coupling affects the quasinormal modes even at linear order in the higher-derivative corrections, due to their isospectrality in general relativity. We provide results for the shifts in the fundamental quasinormal…
Ringing Regularity: Gravitational Perturbations and Quasinormal Modes of Einasto-Supported Black Holes
University of Hradec Králové（赫拉德茨克拉洛韦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National Research University TIIAME（TIIAME国立研究大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；Tashkent State Technical University（塔什干国立技术大学）；Urgench State University（乌鲁奇州立大学）
A distorted black hole radiates gravitational waves in order to settle down in one of the geometries permitted by the no-hair theorem. During that relaxation phase, a characteristic damped ringing is generated. It can be theoretically constructed from the black hole quasinormal frequencies (which govern its oscillating behavior and its decay) and from the associated excitation factors (which determine intrinsically its amplitude) by carefully taking into account the source of the distortion. Here, by considering the Schwarzschild black hole in the framework of massive gravity, we show that the…
We investigate the scalar field system over a charged Weyl black hole, depicted by a parameter $λ$. It is found that the imaginary part of the quasinormal mode spectra is always negative and the perturbation does not increase with the time, indicating that the system is stable under scalar field perturbation. Furthermore, the quasinormal mode spectra and Hawking radiation exhibit a qualitatively similar characteristic in that they both rise with rising $λ$ and approach a constant when $λ$ is large enough. Especially, we would like to emphasize that an exponential decay obviously emerges in the…
We consider the massive scalar field, the Proca field and the Fierz-Pauli field in the Schwarzschild spacetime and we focus more particularly on their long-lived quasinormal modes. We show numerically that the associated excitation factors have a strong resonant behavior and we confirm this result analytically from semiclassical considerations based on the properties of the unstable circular geodesics on which a massive particle can orbit the black hole. The conspiracy of (i) the long-lived behavior of the quasinormal modes and (ii) the resonant behavior of their excitation factors induces int…
Echoes are known as modifications of the usual quasinormal ringing of a black hole at late times because of the deviation of space-time from the initial black-hole geometry in a small region near its event horizon. We consider a class of brane-world model solutions of the Shiromizu-Maeda-Sasaki equations, which describe both black holes and wormholes and interpolate between them via a continuous parameter. In this way the brane-world scenario provides a natural model for wormholes mimicking the black hole behavior if the continuous parameter is chosen near the threshold with a black-hole solut…
We study the perturbative evolution of the static configurations, quasinormal modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell model. We consider first an expansion in harmonic modes and show that it provides a complete solution for the characteristic value problem for the finite perturbations of a static configuration. As a consequence of this completeness we obtain a proof of the stability of static solutions under this type of perturbations. The explicit expression for the mode expansion are then used to obtain numerical values for some of the quasi normal mode c…
The excitation factors of black hole quasinormal modes quantify the $\textit{ease of excitation}$ of the quasinormal modes and are independent of the source of perturbation. We compute the excitation factors of Kerr black holes up to the 20th overtone and find that the 4th, 5th, and 6th overtones have the first three highest excitation factors for intermediate and high spin parameters. This provides an independent confirmation of the importance of overtones that has been confirmed by the fitting data analysis of numerical relativity waveforms beginning around the strain peak amplitude.
We compute scalar quasinormal mode (QNM) frequencies in rotating black hole solutions of the most general class of higher-derivative gravity theories, to quartic order in the curvature, that reduce to General Relativity for weak fields and are compatible with its symmetries. The wave operator governing the QNMs is not separable, but we show one can extract the QNM frequencies by a projection onto the set of spheroidal harmonics. We have obtained accurate results for the quasinormal frequency corrections relative to Kerr for rotating black holes with dimensionless spins up to $\sim 0.7$. We als…
Recently it has been argued that the phantom thin-shell wormholes matched with the Schwarzschild space-time near the Schwarzschild radius ring like Schwarzschild black holes at early times, but differently at late times (arXiv:1602.07309). Here we consider perturbations of the wormhole which was constructed without thin-shells: the Bronnikov-Ellis wormhole supported by the phantom matter and electromagnetic field. This wormhole solution is known to be stable under specific equation of state of the phantom matter. We show that if one does not use the above thin-shell matching, the wormhole, dep…
In the Randall-Sundrum scenario, our universe is a 4-dimensional `brane' living in a 5-dimensional bulk spacetime. By studying the scattering of bulk gravity waves, we show that this brane rings with a characteristic set of complex quasinormal frequencies, much like a black hole. To a bulk observer these modes are interpreted as metastable gravity wave bound states, while a brane observer views them as a discrete spectrum of decaying massive gravitons. Potential implications of these scattering resonances are discussed.
We suggest that quantum transitions of black holes comply with selection rules, analogous to those of atomic spectroscopy. In order to identify such rules, we apply Bohr's correspondence principle to the quasinormal ringing frequencies of black holes. In this context, classical ringing frequencies with an asymptotically vanishing real part ω_R correspond to virtual quanta, and may thus be interpreted as forbidden quantum transitions. With this motivation, we calculate the quasinormal spectrum of neutrino fields in spherically symmetric black-hole spacetimes. It is shown that ω_R->0 for these r…
Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown radiation could be detectable with large signal-to-noise ratio by the Laser Interferometer Space Antenna LISA. If more than one mode is detected, tests of the black hole nature of the source become possible. The detectability of different modes depends on their relative excitation, which in turn depends on the cause of the perturbation (i.e. on the initial da…
A distorted black hole radiates gravitational waves in order to settle down in a smoother geometry. During that relaxation phase, a characteristic damped ringing is generated. It can be theoretically constructed from both the black hole quasinormal frequencies (which govern its oscillating behavior and its decay) and the associated excitation factors (which determine intrinsically its amplitude) by carefully taking into account the source of the distortion. In the framework of massive gravity, the excitation factors of the Schwarzschild black hole have an unexpected strong resonant behavior wh…
The massless scalar wave propagation in the time-dependent BTZ black hole background has been studied. It is shown that in the quasi-normal ringing both the decay and oscillation time-scales are modified in the time-dependent background.
We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal form of a superposition of two effects: exponentially damped oscillations (the quasinormal ringing) and a power law decay (the tail). The quasinormal ringing, which dominates the dynamics for intermediate times, is a linear resonance effect. In contrast, the polynomial tail, which becomes uncovered at late times, is shown to be a \emph{nonlinear} phenomenon.
We study charged black holes in D dimensional AdS space, in the presence of four derivative Weyl correction. We obtain the black hole solution perturbatively up to first as well as second order in the Weyl coupling, and show that first law of black hole thermodynamics is satisfied in all dimensions. We study its thermodynamic phase transition and then calculate the quasinormal frequencies of the massless scalar field perturbation. We find that, here too, the quasinormal frequencies capture the essence of black hole phase transition. Few subtleties near the second order critical point are discu…
The recent reported gravitational wave detection motivates one to investigate the properties of different black hole models, especially their behavior under (axial) gravitational perturbation. Here, we study the quasinormal modes of black holes in Weyl gravity. We derive the master equation describing the quasinormal radiation by using a relation between the Schwarzschild-anti de Sitter black holes and Weyl solutions, and also the conformal invariance property of the Weyl action. It will be observed that the quasinormal mode spectra of the Weyl solutions deviate from those of the Schwarzschild…
We present results obtained by scattering a scalar field off the curved background of a coalescing binary black hole system. A massless scalar field is evolved on a set of fixed backgrounds, each provided by a spatial hypersurface generated numerically during a binary black hole merger. We show that the scalar field scattered from the merger region exhibits quasinormal ringing once a common apparent horizon surrounds the two black holes. This occurs earlier than the onset of the perturbative regime as measured by the start of the quasinormal ringing in the gravitational waveforms. We also use …
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 i…
Stability criteria of nearly extreme black holes in the perturbations level is one of the interesting issues in gravitational systems. Considering the nearly extreme conformal-de Sitter black holes, in this paper, we obtain an exact relation for the quasinormal modes of scalar perturbations. As for stability criteria, we find a lower bound on the event horizon radius which is corresponding to an upper bound on the value of the quasinormal frequencies. In addition, we show that the asymptotic behavior of quasinormal modes gives highly damped modes which is important due to possible connection b…
When the Ringing Stops: Purely Imaginary Modes in the Ringdown Spectrum of Dynamical Black Holes
Sapienza Università di Roma（罗马大学）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；SISSA（的里雅斯特高等研究学院）；INFN Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU – Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；IGAP – Institute for Geometry and Physics（几何与物理研究所）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Universidade de Lisboa（里斯本大学）
Three-dimensional simulations for the merger of binary neutron stars (BNSs) are performed in the framework of full general relativity. We pay particular attention to the black hole (BH) formation case and to the resulting mass of the surrounding disk for exploring possibility for formation of the central engine of short-duration gamma-ray bursts. Hybrid equations of state (EOSs) are adopted mimicking realistic, stiff nuclear EOSs, for which the maximum allowed gravitational mass of cold and spherical neutron stars (NSs), M_sph, is larger than 2M_sun. For the simulations, we focus on BNSs of th…
In this paper, we investigate the evolution of classical wave propagation in the canonical acoustic black hole by numerical method and discuss the details of tail phenomenon. The oscillating frequency and damping time scale both increase with the angular momentum $l$. For the lower $l$, numerical results show the lowest WKB approximation gives the most reliable result. We also find that time scale of the interim region from ringing to tail is not affected obviously by changing $l$.
We employ WKB approximation up to the third order to determine the low-lying quasinormal modes for Weyl neutrino field in R-N black holes, which are the most relevant to the evolution of the field around a black hole in the intermediate stage. It is showed that the quasinormal mode frequencies for Weyl neutrino field in R-N black holes are different from those in Schwartzchild black holes owning to the charge-induced additional gravitation, and the variations of the quasinormal mode frequencies for Weyl neutrino field are similar to those for integral spin fields in R-N black holes.
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 (GUP), 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 m…
Eikonal Ringing, Shadows, Lensing, Grey-Body Factors, and Binding Energy of Asymptotically Flat Regular Black Holes in Phantom Dirac-Born-Infeld Gravity
Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究大学塔什干信息技术与工程研究所基础与应用研究院）；Theoretical Physics Department, Samarkand State University（撒马尔罕国立大学理论物理系）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）
It is well known that the charged scalar perturbations of the Reissner-Nordstrom metric will decay slower at very late times than the neutral ones, thereby dominating in the late time signal. We show that at the stage of quasinormal ringing, on the contrary, the neutral perturbations will decay slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly extreme RN black hole have the same imaginary parts (damping times) for charged and neutral perturbations. An explanation of this fact is not clear but, possibly, is connected with the Choptuik scaling.
We investigate the ringdown waveform and reflectivity of a Lifshitz scalar field around a fixed Schwarzschild black hole. The radial wave equation is modified due to the Lorentz breaking terms, which leads to a diversity of ringdown waveforms. Also, it turns out that Lifshitz waves scattered by the Schwarzschild black hole exhibits superradiance. The Lorentz breaking terms lead to superluminal propagation and high-frequency modes can enter and leave the interior of the Killing horizon where negativity of energy is not prohibited. This allows the Lifshitz waves to carry out additional positive …
Closed photon orbits around isolated black holes are related to important aspects of black hole physics, such as strong lensing, absorption cross section of null particles and the way that black holes relax through quasinormal ringing. When two black holes are present -- such as during the inspiral and merger events of interest for gravitational-wave detectors -- the concept of closed photon orbits still exists, but its properties are basically unknown. With these applications in mind, we study here the closed photon orbits of two different static black hole binaries. The first one is the Maju…
The late stages of the relaxation process of a black hole are expected to depend only on its mass and angular momentum and not on the details of its formation process. Inspired by recent analogue gravity experiments, which demonstrate that certain black hole processes take place in gravitational and hydrodynamical systems alike, we conduct an experiment to search for quasinormal mode oscillations of the free surface of a hydrodynamical vortex flow. Our results demonstrate the occurrence and hint at the ubiquity of quasinormal ringing in nonequilibrium analog black hole experiments.
