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 coefficients of the parametrization. Here we continue this approach by studying the dominant (low-lying) quasinormal modes for such generally parametrized black holes. We show that, due to the hierarchy of parameters, the dominant quasinormal frequencies are also well determined by only the first few coefficients of the expansion for the so-called moderate black-hole geometries. The latter are characterized by a relatively slow change of the metric functions in the radiation zone near the black hole. The nonmoderate metrics, which change strongly between the event horizon and the innermost stable circular orbit are usually characterized by echoes or by the distinctive (from the Einstein case) quasinormal ringing which does not match the current observational data. Therefore, the compact description of a black-hole spacetime in terms of the truncated general parametrization is an effective formalism for testing strong gravity and imposing constraints on allowed black-hole geometries.
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…
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.
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.
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…
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 …
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 w…
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…
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…
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…
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.
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…
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…
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）
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…
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…
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 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 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…
The parametrized black hole quasinormal ringdown formalism is useful to compute quasinormal mode (QNM) frequencies if a master equation for the gravitational perturbation around a black hole has a small deviation from the Regge-Wheeler or Zerilli equation. In this formalism, the deviation of QNM frequency from general relativity can be calculated by small deviation parameters and model independent coefficients. In this paper, we derive recursion relations for the model independent coefficients. Using these relations, the higher order coefficients are written only by the lower order coefficient…
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…
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.
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…
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…
Parametrized quasinormal modes, greybody factors and their correspondence
CENTRA, Departamento de Física, Instituto Superior Técnico - IST, Universidade de Lisboa - UL（里斯本大学高等技术学院物理系CENTRA）；Dipartimento di Fisica, “Sapienza” Universitá di Roma（罗马第一大学物理系）；Sezione INFN Roma1（意大利国家核物理研究所罗马一分部）
Spectral instability of parametrized black hole quasinormal modes in the high-overtone limit via the exact WKB analysis
Osaka Metropolitan University（大阪公立大学）；Osaka Central Advanced Mathematical Institute (OCAMI)（大阪中央先进数学研究所）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学中心交叉理论与数学科学中心）；Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学理学研究科早期宇宙研究中心）；Department of Physics , Kyoto University（京都大学物理系）；Center for Gravitational Physics and Quantum Information,Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理中心引力物理与量子信息）；The Hakubi Center for Advanced Research, Kyoto University（京都大学白兔高级研究中心）
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 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 …
The spectrum of multiple level transitions of the quantum black hole is considered, and the line widths calculated. Initial evidence is found for these higher order transitions in the spectrum of quasinormal modes for Schwarzschild and Kerr black holes, further bolstering the idea that there exists a correspondence principle between quantum transitions and classical ``ringing modes''. Several puzzles are noted, including a fine-tuning problem between the line width and the level degeneracy. A more general explanation is provided for why setting the Immirzi parameter of loop quantum gravity fro…
National Sun Yat-Sen University（国立中山大学）；National Center for Theoretical Sciences（国家理论科学中心）；New York University Abu Dhabi（阿布扎比纽约大学）；CERN（欧洲核子研究组织）；National Technical University of Athens（雅典国立技术大学）；University of Cambridge（剑桥大学）
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 $l$.
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…
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.
Stationary scalar clouds, quasinormal ringing, and observational signatures of (near-)extremal rotating Kalb-Ramond black holes: from the superradiant threshold to EHT bounds
Cyprus International University（塞浦路斯国际大学）；Eastern Mediterranean University（东地中海大学）
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 …
We provide an in-depth investigation of quasinormal-mode oscillations of Kerr black holes with nearly extremal angular momenta. We first discuss in greater detail the two distinct types of quasinormal mode frequencies presented in a recent paper (arXiv:1212.3271). One set of modes, that we call "zero-damping modes", has vanishing imaginary part in the extremal limit, and exists for all corotating perturbations (i.e., modes with azimuthal index m being nonnegative). The other set (the "damped modes") retains a finite decay rate even for extremal Kerr black holes, and exists only for a subset of…
