Quasinormal Mode Spectrum Research Articles

The pseudospectrum and transient of Kaluza-Klein black holes in Einstein-Gauss-Bonnet gravity

Abstract The spectrum and dynamical instability, as well as the transient effect of the tensor perturbation for the so-called Maeda-Dadhich black hole, a type of Kaluza-Klein black hole, in Einstein-Gauss-Bonnet gravity have been investigated in framework of pseudospectrum. We cast the problem of solving quasinormal modes (QNMs) in AdS-like spacetime as the linear evolution problem of the non-normal operator in null slicing by using ingoing Eddington-Finkelstein coordinates. In terms of spectrum instability, based on the generalised eigenvalue problem, the QNM spectrum and $\epsilon$-pseudospectrum has been studied, while the open structure of $\epsilon$-pseudospectrum caused by the non-normality of operator indicates the spectrum instability. In terms of dynamical instability, we introduce the concept of the distance to dynamical instability, which plays a crucial role in bridging the spectrum instability and the dynamical instability. We calculate such distance, named the complex stability radius, as parameters vary. Finally, we show the behaviour of the energy norm of the evolution operator, which can be roughly reflected by the three kinds of abscissas in context of pseudospectrum, and find the transient growth of the energy norm of the evolution operator.

Quasinormal modes of slowly-spinning horizonless compact objects

One of the main predictions of general relativity is the existence of black holes featuring a horizon beyond which nothing can escape. Gravitational waves from the remnants of compact binary coalescences have the potential to probe new physics close to the black hole horizons. This prospect is of particular interest given several quantum-gravity models that predict the presence of horizonless and singularity-free compact objects. The membrane paradigm is a generic framework that allows one to parametrize the interior of compact objects in terms of the properties of a fictitious fluid located at the object’s radius. It has been used to derive the quasinormal mode spectrum of static horizonless compact objects. Extending the membrane paradigm to rotating objects is crucial to constrain the properties of the spinning merger remnants. In this work, we extend the membrane paradigm to linear order in spin and use it to analyze the relationships between the quasinormal modes, the object’s reflectivity, and the membrane parameters. We find a breaking of isospectrality between axial and polar modes when the object is partially reflecting or the compactness differs from the black hole case. We also find that in reflective ultracompact objects some of the modes tend toward instability as the spin increases. Finally, we show that the spin enhances the deviations from the black-hole quasinormal mode spectrum as the compactness decreases. This implies that spinning horizonless compact objects may be more easily differentiated than nonspinning ones in the prompt ringdown. Published by the American Physical Society 2024

Semiclassical imprints on quasinormal mode spectra

Semiclassical imprints on quasinormal mode spectra

Non-spinning tops are stable

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.

Scalar Quasi-Normal Modes of a loop quantum black hole

We compute the Quasi-Normal Mode (QNM) frequencies for scalar perturbations for modified Schwarzschild black holes in Loop Quantum Gravity. We study the singularity-free polymerized metric characterized by two parameters encoding loop quantum effects: the minimal area gap a 0 and the polymeric deformation parameter P. We perform numerical computations using Leaver's continued fraction method and compare our results to other semi-analytical methods and existing literature. We study the effects on the QNM spectrum of variation of both deformation parameters and systematically compare to the standard Schwarzschild case. In particular we find that the scalar fundamental mode is modified from the third decimal for values of P in accordance with the most recent astrophysical constraints. We also show that qualitative differences arise for highly damped modes: on the one hand, a new crossing of the imaginary axis occurs for high values of a 0 and, on the other hand, increasing P produces a positive shift of the real part and an increase of the spacing in imaginary part between modes.

Expansions for semiclassical conformal blocks

We propose a relation the expansions of regular and irregular semiclassical conformal blocks at different branch points making use of the connection between the accessory parameters of the BPZ decoupling equations to the logarithm derivative of isomonodromic tau functions. We give support for these relations by considering two eigenvalue problems for the confluent Heun equations obtained from the linearized perturbation theory of black holes. We first derive the large frequency expansion of the spheroidal equations, and then compare numerically the excited quasi-normal mode spectrum for the Schwarzschild case obtained from the large frequency expansion to the one obtained from the low frequency expansion and with the literature, indicating that the relations hold generically in the complex modulus plane.

Causality and quasi-normal modes in the GREFT

The General Relativity Effective Field Theory (GREFT) introduces higher-derivative interactions to parameterise the gravitational effects of massive degrees of freedom which are too heavy to be probed directly. The coefficients of these interactions have recently been constrained using causality: both from the analytic structure of 4-point graviton scattering and the time delay of gravitational waves on a black hole background. In this work, causality is used to constrain the quasi-normal mode spectrum of GREFT black holes. Demanding that quasi-normal mode perturbations decay faster in the GREFT than in General Relativity—a new kind of causality condition which stems from the analytic structure of 2-point functions on a black hole background—leads to further constraints on the GREFT coefficients. The causality constraints and compact expressions for the GREFT quasi-normal mode frequencies presented here will inform future parameterised gravitational waveforms, and the observational prospects for gravitational wave observatories are briefly discussed.

Near-extremal Kerr-like ECO in the Kerr/CFT correspondence in higher spin perturbations

The Kerr/CFT correspondence has been established to explore the quantum theory of gravity in the near-horizon geometry of an extreme Kerr black holes. The quantum gravitational corrections on the near-horizon region may manifest in form of a partially reflective membrane that replace the horizon. In such modification, the black holes now can be seen as a horizonless exotic compact object (ECO). In this paper, we consider the properties of Kerr-like ECOs in near-extremal condition using Kerr/CFT correspondence. We study the quasinormal modes and absorption cross-section in that background and compare these by using CFT dual computation. The corresponding dual CFT one needs to incorporate finite size/finite N effects in the dual CFT terminology. We also extend the dual CFT analysis for higher spin perturbations such as photon and graviton. We find consistency between properties of the ECOs from gravity sides and from CFT sides. The quasinormal mode spectrum is in line with non-extreme case, where the differences are in the length of the circle, on which the dual CFT lives, and phase shift of the incoming perturbation. The absorption cross-section has oscillatory feature that start to disappear near extremal limit. The particle spin determines the phase shift and conformal weight. We also obtain that the echo time-delay depends on the position of the membrane and extremality of the ECOs.

Example of the convergence of hydrodynamics in strong external fields

The anti-de-Sitter/conformal field theory (AdS/CFT) correspondence is used to provide an estimate of the radius of convergence of the linearized gradient expansion of the hydrodynamic description of N=4 supersymmetric Yang-Mills (SYM) theory minimally coupled to U(1) gauge theory subjected to strong magnetic fields. The results of this work demonstrate that the dispersion relations of hydrodynamic modes continue to converge for magnetic field strengths far beyond those values for which a hydrodynamic description is expected. For magnetic field strengths much larger then the temperature scale the bulk dual interpolates between AdS4+1 and the product of a Bañados-Teitelboim-Zanelli (BTZ) black hole and a two dimensional manifold (BTZ2+1×R2) and may be regarded as a renormalization group flow of the 3+1 dimensional CFT to a 1+1 dimensional CFT. In this regime, we clarify past literature on the quasi-normal mode (QNM) spectrum of bulk scalar fields by introducing a new way to classify the behavior of QNM collisions in the complex frequency and momentum plane. Published by the American Physical Society 2024

Strong Cosmic Censorship in Kerr-Newman-de Sitter

Christodoulou’s formulation of Strong Cosmic Censorship (SCC) holds true for Kerr-de Sitter black holes. On the other hand, Reissner-Nordström-de Sitter black holes violate SCC. We do a detailed scan of the parameter space of Kerr-Newman-de Sitter black holes between these two limiting families, to identify the boundary that marks the transition between solutions that respect and violate SCC. We focus our attention on linear scalar field perturbations. SCC is violated inside a (roughly) ‘spherical’ shell of the parameter space of Kerr-Newman-de Sitter, centred at the corner that describes arbitrarily small extremal Reissner-Nordström-de Sitter solutions. Outside of this region, including the Kerr-de Sitter limit, we identify perturbation modes that decay slow enough to enforce SCC. Additionally, we do a necessary study of the quasinormal mode spectra of Kerr-Newman-de Sitter in some detail. As established in the literature, in the Kerr-de Sitter and Reissner-Nordström-de Sitter limits, we find three families of modes: de Sitter, photon sphere and near-horizon modes. These interact non-trivially away from the Reissner-Nordström-de Sitter limit and display eigenvalue repulsions like in Kerr-Newman black holes.

Physical significance of the black hole quasinormal mode spectra instability

Physical significance of the black hole quasinormal mode spectra instability

Signal of phase transition hidden in quasinormal modes of regular AdS black holes

We discuss the intrinsic relations between thermodynamic phase transitions and quasinormal modes in regular AdS black holes, specifically in the Bardeen and Hayward AdS classes. To this end, we calculate the quasinormal modes of massless scalar field perturbations around small and large black holes via the Horowitz-Hubeny method. By investigating the isobaric and isothermal phase transitions for Bardeen and Hayward AdS black holes in detail, we observe that a dramatic change of quasinormal modes appears near the phase transition point of small and large black holes, and that it corresponds to the swallow tail structure in the plane of Gibbs free energy with respect to pressure. Moreover, by analyzing the evolution of black holes along the coexistence curve of small and large black hole phases, we also observe the dramatic change in quasinormal modes. Such a phenomenon confirms the signal of the phase transition in the quasinormal mode spectrum, which can be understood as a thermodynamic signal hidden in the dynamical spectrum.

Perturbations of spinning black holes in dynamical Chern-Simons gravity: Slow rotation equations

The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the Ψ0 and Ψ4 Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for Ψ0 and Ψ4, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society 2024

Near-extremal Kerr-like ECO in the Kerr/CFT Correspondence

The Kerr/CFT correspondence has been established to explore the quantum theory of gravity in the near-horizon geometry of a extreme Kerr black holes. The horizon can be replaced by partially reflective membrane due to quantum gravitational corrections on the near-horizon region. Because of this modification, black holes now can be seen as a horizonless exotic compact object (ECO). In this work, with Kerr/CFT correspondence we study the properties of Kerr-like ECO in near-extremal condition. We compute the quasinormal modes and absorption cross-section and compare the results with CFT computation. The dual CFT one needs to consider finite size/finite N effects in the dual CFT terminology. We find consistency between properties of the ECOs from gravity side and from CFT side. The quasinormal mode spectrum is in line with non-extreme case with differences in the length of the circle where the dual CFT lives, and phase shift of the incoming perturbation. The absorption cross-section has oscillatory feature that start to vanish in near extremal limit. We also show that the echo time-delay depends on the position of the membrane and extremality of the ECOs.

Quasinormal mode spectrum of the AdS black hole with the Robin boundary condition

We study the quasinormal mode (QNM) spectrum of an asymptotically AdS black hole with the Robin boundary condition at infinity. We consider the Schwarzshild-AdS4 with the flat event horizon as the background spacetime and study its scalar field perturbation. Denoting leading coefficients of slow- and fast-decay modes of the scalar field at infinity as φ 1 and φ 2, respectively, we assume a linear relation between them as ϕ2=cot(θ/2)ϕ1 , where θ is a constant called the Robin parameter and periodic under θ∼θ+2π . In a certain range of the Robin parameter, there is an instability driven by the boundary condition. We also find the holonomy in the QNM spectrum under the parametric cycle of the boundary condition: θ=0→2π . After the one-cycle, nth overtone of the QNM moves to (n−1) th overtone. The fundamental tone of the QNM is swept out to the infinity in the complex plane.

From regular black holes to horizonless objects: quasi-normal modes, instabilities and spectroscopy

We study gravitational and test-field perturbations for the two possible families of spherically symmetric black-hole mimickers that smoothly interpolate between regular black holes and horizonless compact objects accordingly to the value of a regularization parameter.One family can be described by the Bardeen-like metrics, and the other by the Simpson-Visser metric.We compute the spectrum of quasi-normal modes (QNMs) of these spacetimes enlightening a common misunderstanding regarding this computation present in the recent literature.In both families, we observe long-living modes for values of the regularization parameter corresponding to ultracompact, horizonless configurations. Such modes appear to be associated with the presence of a stable photon sphere and are indicative of potential non-linear instabilities.In general, the QNM spectra of both families display deviations from the standard spectrum of GR singular BHs.In order to address the future detectability of such deviations in the gravitational-wave ringdown signal, we perform a preliminary study, finding that third generation ground-based detectors might be sensible to macroscopic values of the regularization parameter.

Scalar QNM spectra of Kerr and Reissner-Nordström revealed by eigenvalue repulsions in Kerr-Newman

Recent studies of the gravito-electromagnetic frequency spectra of Kerr-Newman (KN) black holes have revealed two families of quasinormal modes (QNMs), namely photon sphere modes and near-horizon modes. However, they can only be unambiguously distinguished in the Reissner-Nordström (RN) limit, due to a phenomenon called eigenvalue repulsion (also known as level repulsion, avoided crossing or the Wigner-Teller effect), whereby the two families can interact strongly near extremality. We find that these features are also present in the QNM spectra of a scalar field in KN, where the perturbation modes are described by ODEs and thus easier to explore. Starting from the RN limit, we study how the scalar QNM spectra of KN dramatically changes as we vary the ratio of charge to angular momentum, all the way until the Kerr limit, while staying at a fixed distance from extremality. This scalar field case clarifies the (so far puzzling) relationship between the QNM spectra of RN and Kerr black holes and the nature of the eigenvalue repulsions in KN, that ultimately settle the fate of the QNM spectra in Kerr. We study not just the slowest-decaying QNMs (both for ℓ = m = 0 and ℓ = m = 2), but several sub-dominant overtones as well, as these turn out to play a crucial role understanding the KN QNM spectra. We also give a new high-order WKB expansion of KN QNMs that typically describes the photon sphere modes beyond the eikonal limit, and use a matched asymptotic expansion to get a very good approximation of the near-horizon modes near extremality.

Quasinormal modes of the (2+1)-dimensional Chern–Simons black hole via symmetry

In this study, we adopt an algebraic method to find the spectrum of quasinormal modes for the three-dimensional regular rotating Chern–Simons black hole solution. The latter is a solution to topologically massive gravitoelectrodynamics (TMGE). Due to the fact that the Chern–Simons black hole metric admits four local Killing vectors generating the [Formula: see text] Lie algebra, the solutions to the equations of motion for the fields can be classified by the representations of this algebra. Subsequently, the quasinormal spectrum can be extracted as the infinite tower of descendants of the highest weight mode of [Formula: see text].

From Black Hole Spectral Instability to Stable Observables.

The quasinormal mode spectrum of black holes is unstable under small perturbation of the potential and has observational consequences in time signals. Such signals might be experimentally difficult to observe and probing this instability will be a technical challenge. Here, we investigate the spectral instability of time-independent data. This leads us to study the Regge poles (RPs), the counterparts to the quasinormal modes in the complex angular momentum plane. We present evidence that the RP spectrum is unstable but that not all overtones are affected equally by this instability. In addition, we reveal that behind this spectral instability lies an underlying structure. The RP spectrum is perturbed in such a way that one can still recover stable scattering quantities using the complex angular momentum approach. Overall, the study proposes a novel and complementary approach on the black hole spectral instability phenomena that allows us to reveal a surprising and unexpected mechanism at play that protects scattering quantities from the instability.

U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography

We study the quasi-hydrodynamics of a system with a softly broken U(1) global symmetry using effective field theory (EFT) and holographic methods. In the gravity side, we consider a holographic Proca model in the limit of small bulk mass, which is responsible for a controllable explicit breaking of the U(1) global symmetry in the boundary field theory. We perform a holographic Schwinger-Keldysh analysis, which allows us to derive the form of the boundary effective action in presence of dissipation. We compare our results with the previously proposed EFT and hydrodynamic theories, and we confirm their validity by computing the low-energy quasi-normal modes spectrum analytically and numerically. Additionally, we derive the broken holographic Ward identity for the U(1) current, and discuss the recently proposed novel transport coefficients for systems with explicitly broken symmetries. The setup considered is expected to serve as a toy model for more realistic situations where quasi-hydrodynamics is at work, such as axial charge relaxation in QCD, spin relaxation in relativistic systems, electric field relaxation in magneto-hydrodynamics, or momentum relaxation in condensed matter systems.