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A nonlinear voice from GW250114 ringdown
General Relativity and Quantum Cosmology · Submitted 9 Jan 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here we show the first observational evidence for a set of quadratic quasi-normal modes in the ringdown of the binary black hole merger GW250114, the loudest gravitational-wave event detected to date, enabled by a novel analysis.
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The abstract, sentence by sentence
Gravitational-wave astronomy, by detecting ripples in spacetime, has opened a new window to observe compact objects and probe theories of gravity in the nonlinear strong-field regime. The ringdown signal of a binary black hole merger contains a superposition of damped sinusoids known as quasi-normal modes (Ref.[1]), whose frequencies are completely determined by the mass and spin of the remnant black hole and form the basis of black hole spectroscopy (Refs.[2-4]). A crucial prediction yet to be observationally confirmed is the existence of quadratic quasi-normal modes, which represent fundamental properties associated with wave-wave coupling in general relativity, and the leading mode is predicted to be detectable with next-generation ground-based detectors (Refs.[5-7]) using traditional methods. Here we show the first observational evidence for a set of quadratic quasi-normal modes in the ringdown of the binary black hole merger GW250114, the loudest gravitational-wave event detected to date, enabled by a novel analysis. These nonlinear modes result from the quadratic coupling of the linear $(2,2,n)$ modes with $n\leq3$. Starting the analysis at a time corresponding to four times the remnant mass ($M_\mathrm{f}$) after the merger, the evidence for their presence reaches a Bayes factor of 62. A phenomenological test allowing these modes to deviate from the theoretical prediction rejects the zero-amplitude hypothesis at a significance of 3.4 $\sigma$, while the inferred amplitude and complex frequency are consistent with the prediction of general relativity. This finding provides the first observational evidence of gravitational wave-wave interaction and extends black hole spectroscopy from the linear to the nonlinear regime. It also establishes a new direction for testing the fundamental nonlinear structure of general relativity with the most extreme gravity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Gravitational-wave astronomy, by detecting ripples in spacetime, has opened a new window to observe compact objects and probe theories of gravity in the nonlinear strong-field regime. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | The ringdown signal of a binary black hole merger contains a superposition of damped sinusoids known as quasi-normal modes (Ref.[1]), whose frequencies are completely determined by the mass and spin of the remnant black hole and form the basis of black hole spectroscopy (Refs.[2-4]). | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | A crucial prediction yet to be observationally confirmed is the existence of quadratic quasi-normal modes, which represent fundamental properties associated with wave-wave coupling in general relativity, and the leading mode is predicted to be detectable with next-generation ground-based detectors (Refs.[5-7]) using traditional methods. | gap 0.97 | 0.04 | 0.03 | asserted 0.68 |
| s3 | Here we show the first observational evidence for a set of quadratic quasi-normal modes in the ringdown of the binary black hole merger GW250114, the loudest gravitational-wave event detected to date, enabled by a novel analysis. | contribution 0.63 | 0.97 | 0.93 | asserted 1.00 |
| s4 | These nonlinear modes result from the quadratic coupling of the linear $(2,2,n)$ modes with $n\leq3$. | result 0.46 | 0.55 | 0.07 | asserted 1.00 |
| s5 | Starting the analysis at a time corresponding to four times the remnant mass ($M_\mathrm{f}$) after the merger, the evidence for their presence reaches a Bayes factor of 62. | result 0.93 | 0.96 | 0.06 | asserted 1.00 |
| s6 | A phenomenological test allowing these modes to deviate from the theoretical prediction rejects the zero-amplitude hypothesis at a significance of 3.4 $\sigma$, while the inferred amplitude and complex frequency are consistent with the prediction of general relativity. | result 0.99 | 0.94 | 0.12 | asserted 0.95 |
| s7 | This finding provides the first observational evidence of gravitational wave-wave interaction and extends black hole spectroscopy from the linear to the nonlinear regime. | interpretation 0.98 | 0.94 | 0.79 | asserted 1.00 |
| s8 | It also establishes a new direction for testing the fundamental nonlinear structure of general relativity with the most extreme gravity. | interpretation 0.80 | 0.64 | 0.10 | asserted 0.99 |
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The paper
Original abstract
Gravitational-wave astronomy, by detecting ripples in spacetime, has opened a new window to observe compact objects and probe theories of gravity in the nonlinear strong-field regime. The ringdown signal of a binary black hole merger contains a superposition of damped sinusoids known as quasi-normal modes (Ref.[1]), whose frequencies are completely determined by the mass and spin of the remnant black hole and form the basis of black hole spectroscopy (Refs.[2-4]). A crucial prediction yet to be observationally confirmed is the existence of quadratic quasi-normal modes, which represent fundamental properties associated with wave-wave coupling in general relativity, and the leading mode is predicted to be detectable with next-generation ground-based detectors (Refs.[5-7]) using traditional methods. Here we show the first observational evidence for a set of quadratic quasi-normal modes in the ringdown of the binary black hole merger GW250114, the loudest gravitational-wave event detected to date, enabled by a novel analysis. These nonlinear modes result from the quadratic coupling of the linear $(2,2,n)$ modes with $n\leq3$. Starting the analysis at a time corresponding to four times the remnant mass ($M_\mathrm{f}$) after the merger, the evidence for their presence reaches a Bayes factor of 62. A phenomenological test allowing these modes to deviate from the theoretical prediction rejects the zero-amplitude hypothesis at a significance of 3.4 $\sigma$, while the inferred amplitude and complex frequency are consistent with the prediction of general relativity. This finding provides the first observational evidence of gravitational wave-wave interaction and extends black hole spectroscopy from the linear to the nonlinear regime. It also establishes a new direction for testing the fundamental nonlinear structure of general relativity with the most extreme gravity.
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References
How the literature uses it
11 arXiv papers cite this in 16 sentences
Papers citing it · 14 sentences without a confident label
Cites it as support 1 paper
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The nuisance-extended model family is motivated by recent GW250114 analyses that emphasize early-time prompt or horizon-associated structure and possible nonlinear quadratic content [ref] .
Deterministic Trust Regions for Finite-Window Black-Hole Spectroscopy in GW250114 · Standing assumptions and notation · 0.98
Cites it as background 1 paper
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The quadratic-mode interpretation of Wang et al. [ref] raises a closely related issue from a different direction.
Deterministic Trust Regions for Finite-Window Black-Hole Spectroscopy in GW250114 · Quadratic modes and nonlinear ringdown interpretations · 0.81
What it cites · 39 sentences without a confident label
Uses the method or tool of 6 papers
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For non-precessing binaries, this ratio is computed using the methods outlined in [ref] (summarized in <ref>) and illustrated in <ref>
Quadratic Mode Couplings in Rotating Black Holes and Their Detectability · Method · 0.98
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This is achieved by isolating the likelihood contribution from the inspiral-merger phase and ringdown phase, respectively, by gating and inpainting [ref] data outside the region of interest.
Detecting Gravitational Waves in Data with Non-Gaussian Noise · Introduction · 1.00
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This is achieved by isolating the likelihood contribution from the inspiral-merger phase and ringdown phase, respectively, by gating and inpainting [ref] data outside the region of interest.
A multimode quasi-normal spectrum from a perturbed black hole · Introduction · 1.00
Uses data or values from 9 papers
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We apply this method to the black hole merger event GW250114, the loudest GW detection to date with a network matched-filtering SNR of 80 [ref] by LIGO [ref] , Virgo [ref] and KAGRA [ref] collaboration.
Interferometer design of the KAGRA gravitational wave detector · Introduction · 0.87
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We apply this method to the black hole merger event GW250114, the loudest GW detection to date with a network matched-filtering SNR of 80 [ref] by LIGO [ref] , Virgo [ref] and KAGRA [ref] collaboration.
Advanced Virgo: a 2nd generation interferometric gravitational wave detector · Introduction · 0.87
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We apply this method to the black hole merger event GW250114, the loudest GW detection to date with a network matched-filtering SNR of 80 [ref] by LIGO [ref] , Virgo [ref] and KAGRA [ref] collaboration.
Advanced LIGO · Introduction · 0.87
Cites as background 23 papers
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Beyond the linear QNM spectrum, there are additional non-modal signals [ref] , tail [ref] , dynamical excitation, and nonlinearities present in the ringdown.
Merging black holes with Cauchy-characteristic matching: Computation of late-time tails · Introduction · 0.92
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Beyond the linear QNM spectrum, there are additional non-modal signals [ref] , tail [ref] , dynamical excitation, and nonlinearities present in the ringdown.
GW250114 reveals black hole horizon signatures · Introduction · 0.92
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Beyond the linear QNM spectrum, there are additional non-modal signals [ref] , tail [ref] , dynamical excitation, and nonlinearities present in the ringdown.
2412.06887 · Introduction · 0.92
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