We review the main results obtained in the literature on quasi-normal modes of compact stars and black holes, in the light of recent exciting developments of gravitational wave detectors. Quasi-normal modes are a fundamental feature of the gravitational signal emitted by compact objects in many astrophysical processes; we will show that their eigenfrequencies encode interesting information on the nature and on the inner structure of the emitting source and we will discuss whether we are ready for a gravitational wave asteroseismology.
Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for normal modes and quasi-normal modes. Mode expansions are done and the conserved quantities are studied. Any modes are shown to be separated into two groups, physical modes and unphysical modes, by the zero mode line. Zero modes themselves do not exist as normalizable modes with the correct boundary condition. The allowed physical modes exclude the super-rad…
While black hole perturbation theory predicts a rich quasi-normal mode structure, technical challenges have limited the numerical study of excitations to the fundamental, lowest order modes caused by the coalescence of black holes. Here, we present a robust method to identify quasi-normal mode excitations beyond the fundamentals within currently available numerical relativity waveforms. In applying this method to waveforms of initially non-spinning black hole binaries, of mass ratios 1 to 15, we find not only the fundamental quasi-normal mode amplitudes, but also overtones, and evidence for 2n…
We investigate perturbations of the Schwarzschild geometry using a linearization of the Einstein vacuum equations within a Bondi-Sachs, or null cone, formalism. We develop a numerical method to calculate the quasi-normal modes, and present results for the case $\ell=2$. The values obtained are different to those of a Schwarzschild black hole, and we interpret them as quasi-normal modes of a Schwarzschild white hole.
In this paper we study the fermion quasi-normal modes of a 4-dimensional rotating black-hole using the WKB(J) (to third and sixth order) and the AIM semi-analytic methods in the massless Dirac fermion sector. These semi-analytic approximations are computed in a pedagogical manner with comparisons made to the numerical values of the quasi-normal mode frequencies presented in the literature. It was found that The WKB(J) method and AIM show good agreement with direct numerical solutions for low values of the overtone number $n$ and angular quantum number l.
We study quasi-normal modes of black holes, with a focus on resonant (or quasi-normal mode) expansions, in a geometric frame based on the use of conformal compactifications together with hyperboloidal foliations of spacetime. Specifically, this work extends the previous study of Schwarzschild in this geometric approach to spherically symmetric asymptotically flat black hole spacetimes, in particular Reissner-Nordström. The discussion involves, first, the non-trivial technical developments needed to address the choice of appropriate hyperboloidal slices in the extended setting as well as the ge…
In this paper, we compute quasi-normal modes of ABG black holes (which has a non-linear electrodynamical source) using the WKB methods and AIM. A comparison between the spectrum of QNMs calculated by both methods is made. We analyse how the spectrum of QNMs depends on the black hole parameters, multipole number and overtone number and establish that the ABG black hole is stable against the scalar field.
Black holes have their proper oscillations, which are called the quasi-normal modes. The proper oscillations of astrophysical black holes can be observed in the nearest future with the help of gravitational wave detectors. Quasi-normal modes are also very important in the context of testing of the stability of black objects, the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence and in higher dimensional theories, such as the brane-world scenarios and string theory. This dissertation reviews a number of works, which provide a thorough study of the quasi-normal spectrum of a wide cl…
This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler geometric extensions of the classical theory, these being ways of naturally representing high-energy Lorentz symmetry violations. The second chapter deals with the problem of highly damped quasi-normal modes related to different types of black hole spacetimes. Besides the astrophysical meaning of the quasi-normal modes, there are conjectures about the link betwee…
Efficient parameter inference for gravitational wave signals in the presence of transient noises using temporal and time-spectral fusion normalizing flow
In this work, we implement the semi-analytical WKB method to explore the behaviour of a scalar field on a traversable wormhole space--time with a Casimir--like complexity reported in Eur. Phys. J. C 82, 420 (2022). We estimate the error in the computation of the quasi--normal frequencies of the scalar field at each order in the WKB and show that the order with the best accuracy is not unique. We compute the value of the quasinormal frequencies for the smallest estimated error. As an aside, we find that the imaginary part of the quasinormal modes frequencies approach to zero for the fundamental…
In this paper, we study thermodynamics, quasi-normal modes and thermal fluctuations of a charged black hole with Weyl corrections. We first obtain thermodynamic quantities such as Hawking temperature, entropy, and heat capacity for non-rotating as well as rotating versions of this black hole. We also evaluate temperature through quantum tunneling mechanism which is exactly the same as found through surface gravity. We then discuss the relation between Davies's point and quasi-normal modes. Finally, we investigate the effects of thermal fluctuations on the uncorrected thermodynamic quantities. …
In this work, we use a parametrized theory-agnostic approach that connects the observation of black hole quasi-normal modes with the underlying perturbation equations, with the goal of reconstructing the potential and the coupling functions appearing in the latter. The fundamental quasi-normal mode frequency and its first two overtones are modeled through a second order expansion in the deviations from general relativity, which are assumed to be small but otherwise generic. By using a principal component analysis, we demonstrate that percent-level measurements of the fundamental mode and its o…
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…
We investigate the axial w quasi-normal modes of neutron stars for 18 realistic equations of state in order to study the influence of hyperons and quarks on the modes. The study has been developed with a new method based on Exterior Complex Scaling with variable angle, which allow us to generate pure outgoing quasi-normal modes. A complete study of the junction conditions has been done. We have obtained that w-modes can be used to distinguish between neutron stars with exotic matter and without exotic matter for compact enough stars.
Recent studies of scalar and gravitational waveforms from high-eccentricity, extreme mass-ratio black hole binaries show the presence of quasi-normal bursts (QNB) -- lingering high frequency decaying oscillations (also known as ``wiggles'') -- soon after each periapsis passage. One puzzle associated with these QNB is that in the case of a nearly-extreme rotating central black hole the frequency of the QNB has been found to be in a range which is lower than the corresponding range of relevant quasi-normal modes. We reproduce these results using a different approach and perform a detailed analys…
We have studied quasinormal modes of scalar perturbations of a black hole in massive gravity. The parameters of the theory, such as the mass of the black hole, the scalar charge of the black hole and the spherical harmonic index is varied to see how the corresponding quasinormal frequencies change. We have also studied the massive scalar field perturbations. Most of the work is done using WKB approach while sections are devoted to compute quasinormal modes via the unstable null geodesics approach and the Poschl-Teller approximation. Comparisons are done with the Schwarzschild black hole.
Black hole highly-damped quasi-normal frequencies (QNFs) are very often of the form (offset)} + i n (gap). We have investigated the genericity of this phenomenon for the Schwarzschild--deSitter (SdS) black hole by considering a model potential that is piecewise Eckart (piecewise Poeschl-Teller), and developing an analytic ``quantization condition'' for the highly-damped quasi-normal frequencies. We find that the (offset) + i n(gap) behaviour is common but not universal, with the controlling feature being whether or not the ratio of the surface gravities is a rational number. We furthermore obs…
We compute the axial quasi-normal modes of static neutron stars in scalar tensor theory. In particular, we employ various realistic equations of state including nuclear, hyperonic and hybrid matter. We investigate the fundamental curvature mode and compare the results with those of General Relativity. We find that the frequency of the modes and the damping time are reduced for the scalarized neutron stars. In addition, we confirm and extend the universal relations for quasi-normal modes known in General Relativity to this wide range of realistic equations of state for scalarized neutron stars …
We discuss the quasi-normal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasi-normal frequencies for the wave or higher spin equation on a fixed background geometry described by such black holes, here we compute for the first time the quasi-normal frequencies for the coupled electromagnetic-gravitational linear perturbations. To this purpose, we consider a parametrized family of Lagrangians for the electromagnetic field which contains the Maxwell Lagrangian as a special case. In the Maxwell case, t…
The odd parity gravitational Quasi-Normal Mode spectrum of black holes with non-trivial scalar hair in Horndeski gravity is investigated. We study `almost' Schwarzschild black holes such that any modifications to the spacetime geometry (including the scalar field profile) are treated as small quantities. A modified Regge-Wheeler style equation for the odd parity gravitational degree of freedom is presented to quadratic order in the scalar hair and spacetime modifications, and a parameterisation of the modified Quasi-Normal Mode spectrum is calculated. In addition, statistical error estimates f…
In this paper we study the stability and quasi-normal modes of scalar perturbations of black holes. The static charged black hole considered here is a solution to Born-Infeld electrodynamics coupled to gravity. We conclude that the black hole is stable. We also compare the stability of it with its linear counter-part Reissner-Nordstrom black hole. The quasi-normal modes are computed using the WKB method. The behavior of these modes with the non-linear parameter, temperature, mass of the scalar field and the spherical index are analyzed in detail.
Vacuum quantum fluctuations near horizons are known to yield correlated emission by the Hawking effect. We use a driven-dissipative quantum fluid of microcavity polaritons as an analog model of a quantum field theory on a black-hole spacetime and numerically calculate correlated emission. We show that, in addition to the Hawking effect at the sonic horizon, quantum fluctuations may result in a sizeable stationary excitation of a quasi-normal mode of the field theory. Observable signatures of the excitation of the quasi-normal mode are found in the spatial density fluctuations as well as in the…
We provide an algebraic way to calculate the quasi-normal modes of a black hole, which possesses a hidden conformal symmetry. We construct an infinite tower of quasi-normal modes from the highest-weight mode, in a simple and elegant way. For the scalar, the hidden conformal symmetry manifest itself in the fact that the scalar Laplacian could be rewritten in terms of the $SL(2,R)$ quadratic Casimir. For the vector and the tensor, the hidden conformal symmetry acts on them through Lie derivatives. We show that for three-dimensional black holes, with appropriate combination of the components the …
Highly-damped quasi-normal frequencies are very often of the form omega_n = (offset) + i n (gap). We investigate the genericity of this phenomenon by considering a model potential that is piecewise Eckart (piecewise Poeschl-Teller), and developing an analytic "quantization condition" for the highly-damped quasi-normal frequencies. We find that this omega_n = (offset) + i n (gap) behaviour is generic but not universal, with the controlling feature being whether or not the ratio of the rates of exponential falloff in the two asymptotic directions is a rational number. These observations are of d…
In this work, we calculate the quasi-normal frequencies from a bumblebee traversable wormhole. The bumblebee wormhole model is based on the bumblebee gravity, which exhibits a spontaneous Lorentz symmetry breaking. Supporting by the Lorentz violation parameter $λ$, this model allows the fulfillment of the flare-out and energy conditions, granted non-exotic matter to the wormhole. We analyze the parameters of bumblebee wormhole in order to obtain a Reege-Wheeler's equation with a bell-shaped potential. We obtain the quasi-normal modes (QNMs) via the WKB approximation method for both scalar and …
Born-Infeld electrodynamics has attracted considerable interest due to its relation to strings and D-branes. In this paper the gravitational perturbations of electrically charged black holes in Einstein-Born-Infeld gravity are studied. Effective potentials for axial perturbations are derived and discussed. The quasi normal modes for the gravitational perturbations are computed using the WKB method. The modes are compared with those of the Reissner-Nordstrom black hole. The relation of the quasi normal modes with the non-linear parameter and the spherical index are also investigated. Comments o…
Quasi-normal modes of toroidal, cylindrical and planar black holes in anti-de Sitter spacetimes: scalar, electromagnetic and gravitational perturbations
