Quasinormal Modes Of Black Holes Research Articles

Probing black holes in a dark matter spike of M87 using quasinormal modes

Dark matter density can be significantly enhanced by the supermassive black hole at the galactic center, leading to a structure called dark matter spike. Dark matter spike may change the spacetime properties of black holes that constitute deviations from GR black holes. Based on these interesting background, we construct a set of solutions of black holes in a dark matter spike under the Newtonian approximation and full relativity. Combining the mass model of M87, we study the quasinormal modes of black holes in the scalar field and axial gravitational perturbation, then compared them with Schwarzschild black hole. Besides, the impacts of dark matter on the quasinormal mode of black holes have been studied in depth. In particular, in the axial gravitational perturbation, our results show that the impacts of dark matter spike on the quasinormal mode of black holes can reach up to 10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-4}$$\\end{document}. These new features from quasinormal mode of black holes under the Newtonian approximation and full relativity may provide some help for the establishment of the final dark matter model, and provide a new thought for the indirect detection of dark matter.

Shadow and quasinormal modes of rotating charged black holes in Kalb–Ramond gravity and implications from EHT data

The recent observations of the Event Horizon Telescope for the supermassive black holes M87* and Sgr A* can potentially test gravity theories and acquire further knowledge on black holes and gravity parameters. An essential field of research focuses on the shadow and quasinormal modes of black holes. Therefore, we used the Newman–Janis algorithm to get a rotating charged black hole solution in Kalb–Ramond gravity. Then, we looked at the event horizon radius, the static limit, and the ergoregion of spacetime. We derive the null geodesic equations and the effective potential for photon radial motion. We also investigate how the black hole’s Kalb–Ramond, spin, and charge parameters affect the shadow size and distortion. It is obtained that an increase in the Kalb–Ramond parameter causes a decrease in the radius and increases the distortion of the shadow size. We obtain constraints on black hole charge and spin using the data obtained from Event Horizon Telescope observations of M87* and Sgr A* by testing the effects of the Kalb–Ramond gravity parameter. We examine the energy emission rate using Hawking radiation and demonstrate that a rise in the Kalb–Ramond parameter diminishes this rate. Finally, we calculated and analyzed the typical shadow radius, equatorial, and polar quasinormal modes using the geometric–optic connection between quasinormal mode parameters and conserved quantities along geodesics.

Physical significance of the black hole quasinormal mode spectra instability

Physical significance of the black hole quasinormal mode spectra instability

Searching for ringdown higher modes with a numerical relativity-informed post-merger model

Robust measurements of multiple black hole vibrational modes provide a unique opportunity to characterise gravity in extreme curvature and dynamical regimes, to better investigate the nature of compact objects and search for signs of new physics. We use a numerically-tuned quasicircular non-precessing ringdown model, TEOBPM, and the pyRing analysis infrastructure to perform a time-domain spectroscopic analysis of the third catalog of transient gravitational-wave signals, GWTC-3, searching for higher angular modes. The TEOBPM model effectively includes non-linearities in the early post-merger signal portion, and carries information about the progenitors parameters through time-dependent excitation amplitudes of the black hole quasinormal modes. Such a strategy allows us to accurately model the full post-merger emission, recovering higher signal-to-noise ratios compared to templates based on more agnostic superpositions of damped-sinusoids. We find weak evidence for the presence of (l,m)=(3,3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(l,m)=(3,3)$$\\end{document} [(l,m)=(2,1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(l,m)=(2,1)$$\\end{document}] mode in several events, with the largest Bayes factor in favour of this mode being B≃2.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {B}} \\simeq 2.6$$\\end{document} [B≃1.2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {B}} \\simeq 1.2$$\\end{document}] within the support of the peak time distribution. For GW190521, we observe B≃5.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal {B}} \\simeq 5.1$$\\end{document}, but only for times outside the peak time support reconstructed using the highly accurate NRSur7dq4 model, indicating significant systematics affecting such putative detection. Allowing for deviations from general relativity under the assumption of the presence of two modes, we find tentative support for the Kerr “final state conjecture”. Our work showcases a systematic methodology to robustly identify and characterise higher angular modes in ringdown-only signals, highlighting the significant impact of modelling assumptions and peak time uncertainty on spectroscopic measurements, at current signal-to-noise ratios.

Pseudospectra of holographic quasinormal modes

Quasinormal modes and frequencies are the eigenvectors and eigenvalues of a non-Hermitian differential operator. They hold crucial significance in the physics of black holes. The analysis of quasinormal modes of black holes in asymptotically Anti-de Sitter geometries plays also a key role in the study of strongly coupled quantum many-body systems via gauge/gravity duality. In contrast to normal Sturm-Liouville operators, the spectrum of non-Hermitian (and non-normal) operators generally is unstable under small perturbations. This research focuses on the stability analysis of the spectrum of quasinormal frequencies pertaining to asymptotically planar AdS black holes, employing pseudospectrum analysis. Specifically, we concentrate on the pseudospectra of scalar and transverse gauge fields, shedding light on their relevance within the framework of gauge/gravity duality.

Bernstein spectral method for quasinormal modes and other eigenvalue problems

Spectral methods are now common in the solution of ordinary differential eigenvalue problems in a wide variety of fields, such as in the computation of black hole quasinormal modes. Most of these spectral codes are based on standard Chebyshev, Fourier, or some other orthogonal basis functions. In this work we highlight the usefulness of a relatively unknown set of non-orthogonal basis functions, known as Bernstein polynomials, and their advantages for handling boundary conditions in ordinary differential eigenvalue problems. We also report on a new user-friendly package, called SpectralBP, that implements Berstein-polynomial-based pseudospectral routines for eigenvalue problems. We demonstrate the functionalities of the package by applying it to a number of model problems in quantum mechanics and to the problem of computing scalar and gravitational quasinormal modes in a Schwarzschild background. We validate our code against some known results and achieve excellent agreement. Compared to continued-fraction or series methods, global approximation methods are particularly well-suited for computing purely imaginary modes such as the algebraically special modes for Schwarzschild gravitational perturbations.

Scaling similarities and quasinormal modes of D0 black hole solutions

We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit.The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T9/5. We also present a similar argument for all other Dp-brane geometries.We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an AdS2+9/5× S8 geometry.

Uniform Asymptotic Approximation Method with Pöschl–Teller Potential

In this paper, we study analytical approximate solutions for second-order homogeneous differential equations with the existence of only two turning points (but without poles) by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the Pöschl–Teller (PT) potential, for which analytical solutions are known. Depending on the values of the parameters involved in the PT potential, we find that the upper bounds of the errors of the approximate solutions in general are ≲0.15∼10% for the first-order approximation of the UAA method. The approximations can be easily extended to high orders, for which the errors are expected to be much smaller. Such obtained analytical solutions can be used to study cosmological perturbations in the framework of quantum cosmology as well as quasi-normal modes of black holes.

Quasinormal modes of black holes encircled by a gravitating thin disk

Quasinormal modes of black holes encircled by a gravitating thin disk

Fermionic greybody factors and quasinormal modes of black holes in Kalb–Ramond gravity

In non-minimally coupled Kalb–Ramond (KR) fields, the vacuum expectation value (VEV) leads to spontaneous local Lorentz symmetry violation, resulting in static spherically symmetric solution. In this solution, fermionic greybody factors (GFs) and quasinormal modes (QNMs) are investigated. First, we study the wave dynamics of fermions using the Dirac and Rarita–Schwinger equations. We have derived the equations of effective potential for fermions with different spins. The fermionic GFs radiated by the black holes (BHs) are calculated using rigorous bounds as well as semi-analytic methods. The fermionic QNM of spin- 1/2 of the BHs in the KR gravity was analyzed using the sixth order WKB method. Furthermore, we discuss how Lorentz violating (LV) parameters impact GFs and QNMs. According to our results, the effective potential curve increases significantly when the LV parameter value γ is high. Thus, as the LV parameter γ increases, the bound of the GF and the QNM’s wave oscillation frequency will increase, while the decay rate will slow down.

An implementation of the matrix method using the Chebyshev grid

Abstract In this work, we explore the properties of the matrix method for black hole quasinormal modes on the nonuniform grid. In particular, the method is implemented to be adapted to the Chebyshev grid, aimed at effectively suppressing Runge’s phenomenon. It is found that while such an implementation is favorable from a mathematical point of view, in practice, the increase in precision does not necessarily compensate for the penalty in computational time. On the other hand, the original matrix method, though subject to Runge’s phenomenon, is shown to be reasonably robust and suffices for most applications with a moderate grid number. In terms of computational time and obtained significant figures, we carried out an analysis regarding the trade-off between the two aspects. The implications of the present study are also addressed.

Role of black hole quasinormal mode overtones for ringdown analysis

Role of black hole quasinormal mode overtones for ringdown analysis

Quasinormal modes of black holes in f(Q) gravity

In this work, we have studied the quasinormal modes of a black hole in a model of the type f(Q)=underset{n}{sum }a_{n}left( Q-Q_{0}right) ^{n} in f(Q) gravity by using a recently introduced method known as Bernstein spectral method and confirmed the validity of the method with the help of well known Padé averaged higher order WKB approximation method. Here we have considered scalar perturbation and electromagnetic perturbation in the black hole spacetime and obtained the corresponding quasinormal modes. We see that for a non-vanishing nonmetricity scalar Q_0, quasinormal frequencies in scalar perturbation are greater than those in electromagnetic perturbation scenarios. On the other hand, the damping rate of gravitational waves is higher for electromagnetic perturbation. To confirm the quasinormal mode behaviour, we have also investigated the time domain profiles for both types of perturbations.

Investigating the connection between generalized uncertainty principle and asymptotically safe gravity in black hole signatures through shadow and quasinormal modes

The links between the deformation parameter beta of the generalized uncertainty principle (GUP) to the two free parameters hat{omega } and gamma of the running Newtonian coupling constant of the Asymptotic Safe gravity (ASG) program, has been conducted recently in [Phys. Rev. D 105 (2022) 12, 124054. https://doi.org/10.1103/PhysRevD.105.124054] In this paper, we test these findings by calculating and examining the shadow and quasinormal modes of black holes, and demonstrate that the approach provides a theoretical framework for exploring the interplay between quantum gravity and GUP. Our results confirm the consistency of ASG and GUP, and offer new insights into the nature of black holes and their signatures. The implications of these findings for future studies in quantum gravity are also discussed.

Loop quantum gravity and quasinormal mode of Kerr–Newman black hole

Taking the advantages of loop quantum gravity (LQG), the quasinormal mode frequency spectrum of black holes is studied with the first law of thermodynamics of black holes by calculating the tunneling rate. With the minimum event horizon area interval given by LQG, our results show that one group of the quasinormal mode spectrum for Kerr–Newman black hole depends only on the outer horizon parameters of the black hole. Choosing the minimum spin properly, we derive the quasinormal mode completely consistent with the present results. More importantly, our results show that the quasinormal modes of black holes should have a series of separated frequency spectra, which further proves that the space-time of black holes is quantized.

Quasinormal modes in higher-derivative gravity: Testing the black hole parametrization and sensitivity of overtones

The fundamental quasinormal modes of black holes in higher-derivative gravity given by the Einstein-Weyl action are known to be moderately corrected by the Weyl term. Here we will show that the first several overtones are highly sensitive to even a relatively small Weyl correction, which might be important when representing the earlier stage of the black hole ringdown. In addition, we have solved the problem related to the analytical parametrized approximation of the numerical black hole solution in the Einstein-Weyl theory: In some range of parameters the approximation for the metric developed up to the third order leads to the unusual highly nonmonotonic behavior of the frequencies. We have shown that this problem can be solved via the extension of the parametrization of the metric to higher orders until reaching the regime when the frequencies do not change with further increasing of the order.

Constraining modifications of black hole perturbation potentials near the light ring with quasinormal modes

In modified theories of gravity, the potentials appearing in the Schr\"odinger-like equations that describe perturbations of nonrotating black holes are also modified. In this paper we ask: can these modifications be constrained with high-precision gravitational-wave measurements of the black hole's quasinormal mode frequencies? We expand the modifications in a small perturbative parameter regulating the deviation from the general-relativistic potential, and in powers of $M/r$. We compute the quasinormal modes of the modified potential up to quadratic order in the perturbative parameter. Then we use Markov-chain Monte Carlo methods to recover the coefficients in the $M/r$ expansion in an ``optimistic'' scenario where we vary them one at a time, and in a ``pessimistic'' scenario where we vary them all simultaneously. In both cases, we find that the bounds on the individual parameters are not robust. Because quasinormal mode frequencies are related to the behavior of the perturbation potential near the light ring, we propose a different strategy. Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that the value of the potential and of its second derivative at the light ring can be robustly constrained. These constraints allow for a more direct comparison between tests based on black hole spectroscopy and observations of black hole ``shadows'' by the Event Horizon Telescope and future instruments.

Quasinormal modes from bound states: The numerical approach

It is known that the spectrum of quasinormal modes of potential barriers is related to the spectrum of bound states of the corresponding potential wells. This property has been widely used to compute black hole quasinormal modes, but it is limited to a few ``approximate'' potentials with certain transformation properties for which the spectrum of bound states must be known analytically. In this work we circumvent this limitation by proposing an approach that allows one to make use of potentials with similar transformation properties, but where the spectrum of bound states can also be computed numerically. Because the numerical calculation of bound states is usually more stable than the direct computation of the corresponding quasinormal modes, the new approach is also interesting from a technical point of view. We apply the method to different potentials, including the P\"oschl-Teller potential for which all steps can be understood analytically, as well as potentials for which we are not aware of analytic results but provide independent numerical results for comparison. As a canonical test, all potentials are chosen to match the Regge-Wheeler potential of axial perturbations of the Schwarzschild black hole. We find that the new approximate potentials are more suitable to approximate the exact quasi-normal modes than the P\"oschl-Teller potential, particularly for the first overtone. We hope this work opens new perspectives to the computation of quasinormal modes and finds further improvements and generalizations in the future.

Connections between the Shadow Radius and the Quasinormal Modes of Kerr-Sen Black Hole

The correspondence between the shadow radius and the real part of the quasinormal modes (QNMs) of a Kerr–Sen black hole is studied. By using the equation of the shadow radius of Kerr–Sen black hole and the angular separation constant of the QNMs, the expression of QNMs related to shadow radius is established in the eikonal limit. We found that, our formula can reduce to the previous result of Kerr black hole when Kerr-Sen parameter b sets to zero.

Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The second order in rotation

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals.