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.
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Black hole spectroscopy: from theory to experiment
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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.
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- 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
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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.
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.
Numerical study of cusp formation on horizons in head-on non-spinning black hole mergers, with analysis of mass and multipole behavior at the cusp and a proposed phenomenological model.
citing papers explorer
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GW231123: a Binary Black Hole Merger with Total Mass 190-265 $M_{\odot}$
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.
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Properties of natural polynomials for Schwarzschild and Kerr black holes
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.
-
Unifying the Regge-Wheeler-Zerilli and Bardeen-Press-Teukolsky formalisms on spherical backgrounds
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 and quasinormal mode isospectrality in effective field theories
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.
-
Gravitational-Bumblebee perturbations: Exact decoupling and isospectrality
Bumblebee gravity perturbations decouple exactly into gravitational and vector sectors, with gravitational modes dynamically immune to Lorentz violation and odd-even parities strictly isospectral.
-
Bound-State Resonances of Schwarzschild-de Sitter Black Holes: Analytic Treatment
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.
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Physics informed operator learning of parameter dependent spectra
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.
-
Radiation outer boundary conditions and near-to-far field signal transformations for the Bardeen-Press equation
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.
-
Highly eccentric non-spinning binary black hole mergers: quadrupolar post-merger waveforms
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.
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Novel ringdown tests of general relativity with black hole greybody factors
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.
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Quadratic gravity corrections to scalar QNMs of rapidly rotating black holes
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.
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Quasinormal modes and their excitation beyond general relativity. II: isospectrality loss in gravitational waveforms
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.
-
Modeling the frequency-domain ringdown amplitude of comparable-mass mergers with greybody factors
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.
-
Exceptional Points and Resonance in Black Hole Ringdown
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.
-
Black hole mergers beyond general relativity: a self-force approach
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.
-
Total absorption of tailored incoming signals by black holes
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.
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Black Hole Photon Rings Saturate the Quantum Chaos Bound
Photon rings around black holes saturate the quantum chaos bound via Lyapunov exponents of null geodesics and OTOCs in the near-ring region.
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The third wheel: ringdown and lensing of triple systems
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.
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Pole Skipping, Avoided Crossing, and Resonant Excitation in Kerr Quasinormal Modes near Algebraically Special Frequencies
Kerr QNM anomalies near algebraically special frequencies arise from avoided crossings with resonant excitation and pole skipping due to quasinormal-Matsubara pole-zero cancellations.
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Detectability of avoided crossings in black hole ringdowns
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.
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Ringdown and echoes from compact objects: Debye series and Debye quasinormal modes
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.
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Polarization Analysis of Ringdown Signals
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.
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A cosmology-to-ringdown EFT consistency map for scalar-tensor gravity
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.
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Cusp Formation in Merging Black Hole Horizons
Numerical study of cusp formation on horizons in head-on non-spinning black hole mergers, with analysis of mass and multipole behavior at the cusp and a proposed phenomenological model.
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Pole Structure of Kerr Green's Function
Homogeneous solutions and connection coefficients in the radial Teukolsky equation for Kerr black holes exhibit simple poles at Matsubara frequencies that cancel in the Green's function, along with canceling zero-frequency singularities scaling as ω^{-2l-1}.
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Black Hole Response Theory and its Exact Shockwave Limit
Black hole response theory in WQFT exactly reproduces the Aichelburg-Sexl shockwave metric, geodesics, and the transfer matrix for gravitational-wave scattering off it via post-Minkowskian resummation.
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Cracking Gravitational Wave Multiple Ringdown Modes in Space
FIREFLY algorithm enables 200-fold faster multi-mode ringdown analysis for space-borne gravitational wave detectors while remaining compatible with time-delay interferometry.
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Geometrically Regular Black Holes with Hedgehog Scalar Hair
A continuous family of asymptotically flat, geometrically regular black holes with hedgehog scalar hair exists in a minimally coupled GR-scalar-three-form theory.
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Bilinear products and the orthogonality of quasinormal modes on hyperboloidal foliations
Bilinear products for black hole quasinormal modes on hyperboloidal foliations are divergent due to CPT transformations but can be regularized to define orthogonal modes and excitation coefficients.
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Ringing of rapidly rotating black holes in effective field theory
Leading-order cubic-curvature corrections to scalar quasinormal modes of black holes with spins up to 0.99M are computed numerically for modes up to l=5 with relative errors below 10^{-4}.
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Correspondence between quasinormal modes and grey-body factors of Schwarzschild--Tangherlini black holes
Quasinormal modes correspond well to grey-body factors for vector and tensor perturbations of Schwarzschild-Tangherlini black holes in all dimensions, but fail for scalar l=2 modes in D≥7 because of multiple potential barriers.
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Nonlinear tails of massive scalar fields around a black hole
Nonlinear tails of massive scalar fields around black holes decay at the same rate as linear tails during intermediate times, independent of sources or initial conditions.
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The relativistic restricted three-body problem: geometry and motion around tidally perturbed black holes
Increasing tidal deformation around a black hole drives bound geodesics through weak chaos, plunging, unbinding, and eventual depletion of all bound motion, with semi-analytic critical amplitudes for each transition.
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Plunge-Merger-Ringdown Tests of General Relativity with GW250114
GW250114 data constrains GR deviations in merger amplitude to 10% and frequency to 4% at 90% CL, with first bounds on the (4,4) mode frequency at 6%.
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Probing higher curvature gravity via ringdown with overtones
Higher-curvature terms deform the near-horizon potential of spherically symmetric black holes, producing progressively larger shifts in overtone quasinormal frequencies that remain detectable in ringdown waveforms when the fundamental mode stays close to its GR value.
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Quasinormal modes of rotating black holes beyond general relativity in the WKB approximation
Higher-order WKB accurately computes quasinormal mode frequencies for rotating black holes beyond general relativity, with errors below current GW measurement precision for GW250114.
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Quasinormal modes of Reissner-Nordstr\"om-AdS black holes under physical field-vanishing boundary conditions
The authors introduce physical field-vanishing boundary conditions for RN-AdS black holes, translate them to master-function conditions, and compute quasinormal frequencies that show new spectral features.
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Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
Excitation factors of long-lived quasinormal modes in horizonless compact objects scale with their small imaginary frequency, suppressing early contributions and producing a hierarchy where prompt ringdown uses ordinary modes and late echoes use cavity modes.
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Reflectionless and echo modes in asymmetric Damour-Solodukhin wormholes
In asymmetric Damour-Solodukhin wormholes, reflectionless and echo modes share asymptotic spectral properties parallel to the real frequency axis with matching spacing, and reflectionless modes lie closer to the axis yielding larger echo amplitudes.
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Black Hole Spectroscopy and Tests of General Relativity with GW250114
GW250114 data confirm the remnant is consistent with a Kerr black hole and bound the dominant quadrupolar mode frequency to within a few percent of the GR prediction, with constraints tighter than prior multi-event catalogs.
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Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes
The work reviews a Hamiltonian formalism for perturbations of nonrotating black holes, interprets Darboux transformations as canonical transformations, extends the axial-polar correspondence to polar cases, and demonstrates mixing transformations between axial and polar master functions.
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Ringdown Signatures of Dehnen Dark Matter Halos: Fluid Modes and Detectability with Space-Based Detectors
Numerical ringdown waveforms for black holes in Dehnen dark matter profiles are generated and analyzed for detectability and parameter inference using second-generation TDI in space-based detectors such as LISA, Taiji, and TianQin.
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Impact of sky localization uncertainty on ringdown inference
Properly accounting for sky localization uncertainty in ringdown inference widens mode-amplitude posteriors, avoids bias from fixed point estimates, and leaves amplitude ratios robust for Kerr spectroscopy.
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Dynamical quasinormal mode excitation II: propagation and convergence in Schwarzschild
Refined propagation prescription for quasinormal modes excited by plunging particles confirms a bounce radius at r_*=0 and yields accurate reproduction of the post-bounce oscillatory waveform component from first principles.
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Nucleosynthesis in the fast ejecta of a neutron star merger
Free neutrons survive r-process freeze-out in fast ejecta of neutron star mergers and their beta-decay heating produces a visible early kilonova precursor for mass fractions above ~0.05.
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Perturbations in the parametrized wormhole spacetime and their related quasinormal modes
Observationally constrained galactic wormhole models show quasinormal mode damping rates more sensitive to galactic compactness than deformation parameters, while oscillation frequencies remain comparatively stable.
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Ringdown Analysis of GW250114 with Orthonormal Modes
Orthonormal QNM analysis of GW250114 raises the significance of the first overtone of the ℓ=m=2 mode from 82.5% to 99.9% and detects no significant deviation from Kerr predictions.
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Can wormholes have vanishing Love numbers?
For a specific R=0 wormhole, the magnetic Love number for ℓ=2 vanishes to linear order in the regularization parameter under static axial gravitational perturbations.
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Emergent structure in the binary black hole mass distribution and implications for population-based cosmology
B-spline agnostic reconstruction of binary black hole masses from GWTC-4.0 reveals multiple features and a logarithmic hierarchy that impacts Hubble constant measurements, with a low-mass subpopulation isolation method to mitigate systematics.
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Spectroscopy of analogue black holes using simulation-based inference
Simulation-based inference reliably extracts physical parameters from noisy spectra of analogue black holes.