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.
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Black hole spectroscopy: from theory to experiment
33 Pith papers cite this work. Polarity classification is still indexing.
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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 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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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.
The early growth of the weakly responding scalar component in an unstable Q-ball hairy black hole is dominated by a second-order QNM sourced by the linear unstable mode, even while evolution remains perturbative.
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.
Viscous neutron stars have new families of axial oscillation modes without perfect-fluid counterparts, featuring mode avoidance and long-lived modes.
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.
New stationary vectorized black holes exist in Einstein-vector-Gauss-Bonnet theory, including charged spherical, uncharged axial with magnetic moments, and rotating solutions bounded by Kerr and static cases.
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.
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.
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}.
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.
FIREFLY algorithm enables 200-fold faster multi-mode ringdown analysis for space-borne gravitational wave detectors while remaining compatible with time-delay interferometry.
A continuous family of asymptotically flat, geometrically regular black holes with hedgehog scalar hair exists in a minimally coupled GR-scalar-three-form theory.
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.
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}.
Numerical simulations of head-on black hole mergers reveal cusp formation on horizons, with mass and multipole moments behaving in ways that link initial and final black hole states via a phenomenological model.
Observationally constrained galactic wormhole models show quasinormal mode damping rates more sensitive to galactic compactness than deformation parameters, while oscillation frequencies remain comparatively stable.
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.
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.
Computations for a new black hole metric with magnetic charge and Hernquist halo show that charge raises QNM frequencies while the halo lowers them, with similar opposing effects on shadow size and neutrino annihilation efficiency.
citing papers explorer
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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.
-
Early-Time Nonlinear Growth in an Unstable Q-Ball Hairy Black Hole
The early growth of the weakly responding scalar component in an unstable Q-ball hairy black hole is dominated by a second-order QNM sourced by the linear unstable mode, even while evolution remains perturbative.
-
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.
-
Axial Oscillations of Viscous Neutron Stars
Viscous neutron stars have new families of axial oscillation modes without perfect-fluid counterparts, featuring mode avoidance and long-lived modes.
-
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.
-
Stationary Einstein-vector-Gauss-Bonnet black holes
New stationary vectorized black holes exist in Einstein-vector-Gauss-Bonnet theory, including charged spherical, uncharged axial with magnetic moments, and rotating solutions bounded by Kerr and static cases.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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.
-
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}.
-
Cusp Formation in Merging Black Hole Horizons
Numerical simulations of head-on black hole mergers reveal cusp formation on horizons, with mass and multipole moments behaving in ways that link initial and final black hole states via a phenomenological model.
-
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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Quasinormal Modes and Neutrino Energy Deposition for a Magnetically Charged Black Hole in a Hernquist Dark Matter Halo
Computations for a new black hole metric with magnetic charge and Hernquist halo show that charge raises QNM frequencies while the halo lowers them, with similar opposing effects on shadow size and neutrino annihilation efficiency.
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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.
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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.
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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.
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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.
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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.
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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.
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Pair-Dependent Drift of Kerr Neighboring-Overtone Gap Minima
Kerr overtone frequency gaps exhibit pair-dependent spin locations for their interior minima.
- Bound-State Resonances of Schwarzschild-de Sitter Black Holes: Analytic Treatment