A new gravitational wave event reveals a binary black hole merger with total mass 190-265 solar masses, indicating black holes can form via gravitational-wave driven mergers beyond standard stellar channels.
hub Canonical reference
Black hole spectroscopy: from theory to experiment
Canonical reference. 94% of citing Pith papers cite this work as background.
76
Pith papers citing it
Background
94% of classified citations
abstract
The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based gravitational-wave detectors.
hub tools
citation-role summary
background 33
citation-polarity summary
claims ledger
- abstract The "ringdown" radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinorm
co-cited works
roles
background 33representative citing papers
Natural polynomials for Schwarzschild and Kerr quasinormal modes are Pollaczek-Jacobi polynomials with complex parameters, with recurrence peaking at the physical overtone index for Schwarzschild.
A self-dual curvature formulation unifies the Regge-Wheeler-Zerilli and Bardeen-Press-Teukolsky equations on spherical backgrounds as components of one tensorial curvature equation.
Gravitational electric-magnetic duality at the light ring organizes and preserves quasinormal mode isospectrality in GR and selects duality-invariant higher-derivative corrections in effective field theories.
Bumblebee gravity perturbations decouple exactly into gravitational and vector sectors, with gravitational modes dynamically immune to Lorentz violation and odd-even parities strictly isospectral.
SdS black holes support only a finite number of bound-state resonance levels with closed-form energies, while asymptotically flat Schwarzschild black holes have infinitely many that delocalize without bound.
DeepOPiraKAN learns parameter-to-spectrum mappings via operator learning and achieves relative errors of O(10^{-6}) to O(10^{-4}) for Kerr black hole quasinormal modes up to n=7 when benchmarked against Leaver's method.
Exact transparent radiation boundary conditions and near-to-far field teleportation kernels are derived for the Bardeen-Press equation, approximated via exponential sums with error bounds, and shown to eliminate late-time artifacts in time-domain solvers.
Polynomial models for the (2,2) post-merger waveform amplitudes of eccentric non-spinning binary black holes are constructed from numerical-relativity data as functions of symmetric mass ratio and two merger-time dynamical parameters.
GreyRing model based on greybody factors reproduces numerical relativity ringdown signals with mismatches of order 10^{-6} and enables a new post-merger consistency test of general relativity applied to GW250114.
Leading-order deviations from general relativity in scalar quasinormal modes of rotating black holes are computed numerically up to dimensionless spins of 0.99 in quadratic-curvature scalar-tensor theories.
In a beyond-GR cubic-curvature model, loss of isospectrality makes it generally difficult to identify the two fundamental quasinormal modes from black hole ringdown time series, though evidence for a non-GR mode is sometimes possible.
A four-parameter greybody factor model reproduces the frequency-domain ringdown amplitude of comparable-mass aligned-spin mergers with mismatches of order 10^{-5}, improving existing models by two orders of magnitude.
An exceptional-point framework for black-hole ringdown characterizes resonances near avoided crossings, demonstrates enhanced mode contributions in the time domain, and identifies the EP frequency as the physically relevant observable.
Self-force theory is extended to compute merger and ringdown waveforms in beyond-GR black hole binaries under the extreme mass-ratio approximation, with first calculations of self-force corrections to the merger waveform.
Tailored temporal modulation of incoming signals enables complete absorption by black holes via excitation of complex-plane resonances, storing energy for later release through virtual absorption modes.
Photon rings around black holes saturate the quantum chaos bound via Lyapunov exponents of null geodesics and OTOCs in the near-ring region.
SPRING framework propagates pre-merger information into spectral-level ringdown inference, improving Bayesian support for an agnostic two-damped-sinusoid model on GW250114 by ΔlnB ~5-10 while keeping remnant posteriors consistent with IMR estimates.
Numerical relativity simulations of triple black hole systems reveal redshift effects and gravitational lensing in ringdown signals from head-on mergers, with no additional black hole formation from amplified waves.
Kerr QNM anomalies near algebraically special frequencies arise from avoided crossings with resonant excitation and pole skipping due to quasinormal-Matsubara pole-zero cancellations.
Bayesian analysis finds individual QNM frequencies near avoided crossings hard to resolve even under optimistic conditions, though collective AC waveform signatures may remain detectable if those modes dominate and slower-mode contamination is minimal.
Introduces Debye series and Debye-QNMs to decompose waveforms from Schwarzschild-star models, achieving early-time convergence and organizing ringdown plus echo packets into individual propagation channels.
Constrained polarization model for Kerr ringdown modes enables inclination inference from two-detector data for non-precessing mergers but introduces biases when applied to precessing systems.
An EFT consistency map transports cosmology-conditioned posteriors from scalar-tensor FLRW backgrounds to black-hole quasinormal-mode kernels, showing tensor-speed effects fall below ringdown detectability while other operators remain potentially active near black holes.
citing papers explorer
-
Spectroscopy of analogue black holes using simulation-based inference
Simulation-based inference reliably extracts physical parameters from noisy spectra of analogue black holes.
-
Prompt Response from Plunging Sources in Schwarzschild Spacetime
The prompt response is ~1.2 times stronger than quasinormal mode excitation during inspiral and enables 99% accurate reconstruction of the full inspiral-merger-ringdown waveform when combined with other components.
-
Quasinormal modes of coupled metric-dilaton perturbations in two-dimensional stringy black holes
Coupled intrinsic perturbations of the MSW black hole yield complex quasinormal frequencies with negative imaginary parts confirming stability and non-zero real parts indicating oscillatory behavior, with damping rates decreasing as the central charge parameter increases.
-
Autoencoder-Based Parameter Estimation for Superposed Multi-Component Damped Sinusoidal Signals
Autoencoder uses latent space to estimate parameters of multi-component damped sinusoids in noise with high accuracy even for weak or opposing-phase components.
-
Can Oscillatory and Persistent Nonlinearities Be Bridged in Black Hole Ringdown?
Quadratic quasinormal modes and the memory effect in black hole ringdown are related through bridge coefficients that depend primarily on remnant black hole parameters.
-
Confronting eikonal and post-Kerr methods with numerical evolution of scalar field perturbations in spacetimes beyond Kerr
Numerical simulations benchmark the eikonal and post-Kerr approximations for quasinormal modes in deformed Kerr spacetimes, quantifying their errors relative to expected observational precision.
-
Quasinormal mode/grey-body factor correspondence for Kerr black holes
WKB analysis of the Teukolsky equation establishes a quasinormal-mode to greybody-factor correspondence for Kerr black holes that holds in the eikonal limit for gravitational perturbations and matches numerics at high angular momentum.
-
Gravitational Atoms from Topological Stars
Bound states of a massive scalar field around topological stars form strictly normal modes, producing a hydrogen-like spectrum when the Compton wavelength exceeds the star size and localized states otherwise.
-
Green function of the P\"{o}schl-Teller potential
Exact time-domain Green function computed for the Pöschl-Teller approximation to black-hole perturbation potentials, revealing additional early-time exponentially growing modes and a light-cone plus historical waveform decomposition.
-
Impact of facility timing and coordination for next-generation gravitational-wave detectors
Simulations of ET and CE networks show delays degrade localization metrics far more than SNR, with LIGO India greatly reducing the impact for multi-messenger and stochastic searches.
-
Quasinormal modes of Kerr-Newman black holes: revisiting the Dudley-Finley approximation
Reassessment of the Dudley-Finley decoupling approximation for Kerr-Newman quasinormal modes with direct comparisons to the coupled system and new analysis of near-extremal zero-damped modes.
-
GW250114: testing Hawking's area law and the Kerr nature of black holes
GW250114 data confirm the remnant black hole ringdown frequencies lie within 30% of Kerr predictions and that the final horizon area is larger than the sum of the progenitors' areas to high credibility.
-
Echoes and quasinormal modes of asymmetric black bounces
Computes quasinormal modes and echoes for black bounce solutions, finding echoes only in certain symmetric horizonless cases and none in asymmetric models that recover Reissner-Nordström externally.
-
Black-Hole Echo Resonance Spectra and Source Dependence in a Controlled Transfer-Function Model
Proves rigorous O(L^{-2}) localization estimates for resonance spectra in a compactly supported transfer-function model of black-hole echoes with explicit normalizations.
-
Total transmission modes in draining bathtub model with vorticity
Numerical spectra of total transmission modes in the draining bathtub model with vorticity can have positive or negative imaginary parts depending on parameters, with higher overtones exhibiting pronounced spectral mobility.
-
Pair-Dependent Drift of Kerr Neighboring-Overtone Gap Minima
Kerr overtone frequency gaps exhibit pair-dependent spin locations for their interior minima.
-
GWTC-4.0: Tests of General Relativity. III. Tests of the Remnants
Gravitational wave remnants from GWTC-4.0 binary mergers are consistent with general relativity Kerr black hole predictions, with no evidence for post-merger echoes.
-
Squeezed Quasinormal Modes from Nonlinear Gravitational Effects
Estimates one percent squeezing in gravitational waves from nonlinear effects in the ringdown phase of black hole mergers using higher harmonic amplitude ratios.
-
Quasinormal modes and grey-body factors of axial gravitational perturbations of regular black holes in asymptotically safe gravity
Axial quasinormal modes of regular black holes in asymptotically safe gravity are weakly affected by the deviation parameter for the fundamental mode but show notable deviations for higher overtones, with strong agreement between grey-body factors and QNMs for large multipole numbers.
-
On the impossibility of observational confirmation of black holes
No observational data can confirm the existence of black holes because general relativity imposes fundamental limits on what can be established about them.
-
GWTC-5.0: An Introduction to Version 5.0 of the Gravitational-Wave Transient Catalog
GWTC-5.0 is a data release documenting over 300 gravitational-wave events from compact binary mergers observed through early 2025.
- Bouncing singularities in Schwarzschild: a geometric origin of the QNM convergence region
- Early-Time Nonlinear Growth in an Unstable Q-Ball Hairy Black Hole
- Breaking Parameter Degeneracies in a Magnetically Charged Black Hole Embedded in a Hernquist Dark-Matter Halo: A Multi-Observable Analysis
- Axial Oscillations of Viscous Neutron Stars
- Stationary Einstein-vector-Gauss-Bonnet black holes