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Scientists test general relativity (GR) by measuring the gravitational waves emitted as a newly merged black hole settles, then checking whether the signal’s frequencies and decay match GR’s predictions. They also compare the remnant black hole inferred from ringdown with the remnant predicted from the earlier inspiral and merger. Agreement supports GR in the events and measurements analyzed; it does not prove that GR applies in every setting.
What black-hole ringdown is
A binary black-hole gravitational-wave signal is commonly divided into three stages: inspiral, merger and ringdown. During inspiral, the two black holes orbit one another and lose energy by emitting gravitational waves. They then merge into a single remnant. That newly formed black hole is initially distorted, and the waves it emits as it settles into a stable state make up the ringdown.
The signal’s ringdown can be understood, approximately, as damped oscillations: the oscillations fade rather than continuing indefinitely. The analogy of a struck bell can help explain the fading tones, but a black hole is not a bell. Its ringdown is a gravitational-wave signal governed by the remnant’s properties and by gravity.
In GR, a settled rotating black hole is described by its mass and spin. Those parameters determine the expected frequencies and damping times of its quasi-normal modes (QNMs). A mode is one component of the damped signal: frequency describes how quickly it oscillates, while damping time describes how quickly it fades. Researchers test whether the measured signal is compatible with the mode properties predicted for the remnant, rather than treating any observed oscillation as an arbitrary tone. As LIGO’s O3a general-relativity summary puts it, “In a similar way, general relativity requires the black hole ringdown to exhibit particular frequencies and damping times.”
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How a ringdown test works
1. Identify the part of the signal being tested
Researchers analyze the measured gravitational-wave signal and distinguish its phases. The inspiral and merger contain information about the binary before and during coalescence; the post-merger signal contains information about the remnant settling. The test depends on which part of the waveform is used, because different analyses ask different questions.
A ringdown-focused analysis looks for the damped oscillations after merger. Another approach separates the lower-frequency inspiral from the higher-frequency post-inspiral portion, which includes merger and ringdown. In that consistency test, researchers infer the final black hole’s mass and spin from each portion and check whether the estimates overlap as GR predicts.
These approaches use different slices of the same event. A ringdown-only analysis asks whether the post-merger oscillations fit the expected remnant spectrum. An inspiral-merger-ringdown consistency test instead asks whether information from the earlier and later portions points to compatible final properties. The latter is most useful when each portion has enough signal to analyze independently; it is not simply a second way of measuring the same ringdown tones.
2. Infer the remnant’s modes and properties
Scientists estimate or constrain features of the post-merger signal, including its mode frequencies and damping times. They then compare those measurements with the spectrum expected under GR for a remnant with the inferred mass and spin. The modes are not arbitrary tones: in GR, the remnant’s mass and spin fix their expected values.
In practice, the measured signal is finite and noisy, so an analysis determines which mode properties are supported by the data and how uncertain those estimates are. It is a comparison between measured or constrained signal properties and a predicted spectrum, not a requirement that observations reproduce exact values without uncertainty. Researchers can also test parameterized changes to waveform predictions to ask whether the data favor departures from the standard GR description.
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When only one harmonic can be measured, it can still support a consistency check. Researchers can compare the remnant properties inferred from that signal with properties predicted from the earlier phases. The test becomes more demanding when more than one harmonic is resolved, because each mode can provide another estimate of the remnant’s parameters.
3. Check whether the signal is self-consistent
The inspiral-merger-ringdown test asks whether the final black hole inferred from the earlier, lower-frequency part of the signal agrees with the final black hole inferred from the higher-frequency post-inspiral part. In GR, both portions describe the same physical event and therefore should yield compatible remnant properties. The comparison is most informative when each segment has enough signal for a separate analysis.
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Why multiple modes matter for the no-hair test
The no-hair idea, as tested in this setting, is that a settled Kerr black hole is fully characterized by mass and spin. If researchers resolve multiple ringdown harmonics, they can infer mass and spin from distinct modes and ask whether those estimates describe one consistent Kerr black hole. This is a more direct test than checking a single mode against properties inferred before merger.
There is an important practical distinction between detecting a mode and resolving enough independent mode information to compare estimates. A single harmonic is usually the case and can be checked against remnant parameters inferred during the earlier event. Multiple resolved harmonics allow a cross-mode consistency test, but ringdown is short and the signal may not support that more demanding analysis.
LIGO’s O4b general-relativity summary explains the distinction: “Detecting a single harmonic —which is usually the case— allows for consistency checks with parameters inferred before and during the merger, while resolving more than one harmonic and checking the consistency of the black hole parameters inferred from each provides a direct test of the no-hair theorem.” A single detected harmonic is therefore useful, but it does not provide the same cross-mode test as multiple resolved harmonics.
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Examples from observed mergers
GW150914: consistency across the merger
In its 2016 analysis of GW150914, the LIGO/Virgo Collaboration reported that the final remnant’s mass and spin inferred from low-frequency inspiral data and high-frequency post-inspiral data were mutually consistent. The collaboration also found that data after the signal peak were consistent with the least-damped QNM inferred from the remnant’s mass and spin. These findings were reported in its GW150914 general-relativity tests paper.
GW150914: modes and no-hair tests
A separate 2019 analysis by Isi and colleagues examined GW150914 using data beginning at the signal peak. The authors reported evidence at 3.6 sigma for the fundamental QNM and at least one overtone. They characterized the no-hair test based on comparing the remnant’s mass and spin at approximately the 10% level, and an independent check of the first-overtone frequency at approximately the 20% level. Those figures describe that specific analysis of GW150914; they are not general precision claims for ringdown tests. The signal-start choice and the particular comparison matter when interpreting the result. See the paper, “Testing the No-Hair Theorem with GW150914”.
Recent events and catalog results
The LIGO Scientific Collaboration’s O4b summary reports a subdominant harmonic alongside the dominant harmonic in ringdown analyses of GW250114 and GW240621. It describes GW250114 as enabling particularly precise constraints on possible ringdown deviations. This does not mean every event yields multiple measurable modes: resolving them depends on the signal available in the observation.
The LIGO-Virgo-KAGRA Collaboration’s GWTC-4.0 remnant-tests paper record describes an analysis including 42 events from the first part of the fourth observing run along with earlier events. The selected confident signals were seen in at least two detectors and met a false-alarm-rate threshold of no more than 10−3 per year. The paper record describes three ringdown tests and four echo tests. Among the GWTC-4.0 events, it identifies GW231226_101520 as providing the tightest single-event constraint on the damping time of the dominant (2, 2, 0) mode in the frequency-domain ringdown analysis.
At catalog level, the paper reports the GR prediction at the boundary of a 98.6% (99.3%) credible region in a hierarchical analysis, with bootstrap ranges reflecting the finite sample. It also notes that the apparent significance decreases when GW250114 is included, and concludes there is no strong evidence for a deviation from GR. A boundary result in a statistical analysis is not the same as establishing that GR is false; the reported finite-sample ranges are part of interpreting the catalog result.
Other ringdown searches: deviations and echoes
Not every test is simply a comparison of measured modes with the standard prediction. Researchers also test parameterized changes to waveform predictions and search for post-merger echoes. These tests ask related but distinct questions: a mode test compares frequencies or damping times with the expected spectrum, a waveform-deviation test checks specified changes to the prediction, and an echo search looks for an additional post-merger feature.
Echoes are not expected in standard-GR black-hole ringdown, but have been proposed in some alternatives to the usual black-hole picture. The GWTC-4.0 remnant paper reports no evidence for echoes in the analyzed events. That non-detection constrains proposed possibilities only to the extent allowed by the sensitivity and assumptions of that particular search. It does not rule out every model that could produce echoes under other conditions.
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Ringdown is short, and many events do not have enough signal-to-noise ratio to resolve multiple modes. Even when a test can be performed, its precision depends on the signal and on how the analysis separates and models the waveform. A result described as consistent with GR means that the analyzed data do not require a departure at the sensitivity of that test; it is not proof that all alternative theories are impossible.
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- Detector coverage: the GWTC-4.0 selection described in the paper record required confident signals in at least two detectors, while the available signal still determines how much can be inferred about a particular event.
- Modeling and calibration: waveform approximations and instrumental calibration can affect inferred deviations, so a claimed departure must be interpreted in light of those assumptions.
- Finite samples: catalog-level conclusions have statistical uncertainty because they combine a limited number of events; the GWTC-4.0 analysis reports bootstrap ranges for its finite sample.
Evidence quality is therefore not captured by one number alone. Signal strength, which parts of the waveform can be analyzed, detector coverage, calibration, modeling choices and statistical uncertainty all affect how strongly a particular test can constrain a departure. A result from one event, one mode or one kind of search should be read in that context rather than treated as a universal verdict.
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For these reasons, the careful conclusion is specific: a given analysis found its data consistent with GR, or found no evidence for a deviation, within its measurement limits. The strength of a single event’s test should not be generalized to every black hole or every regime of gravity.
How to read a ringdown result
When evaluating a reported result, first identify which data were analyzed and what quantity was measured. A study using the post-merger signal alone is not the same test as one comparing inspiral and post-inspiral remnant estimates. Then check whether it measured one dominant harmonic or resolved multiple modes, and whether its conclusion concerns mass and spin, frequency, damping time, waveform deviations or echoes.
- One harmonic: useful for consistency with parameters inferred earlier in the event, but not the same as comparing independent remnant estimates from multiple modes.
- Several harmonics: can test whether different mode estimates fit one Kerr black hole, if the signal is sufficiently informative.
- Catalog analysis: tests whether a pattern across events supports a departure, while accounting for the sample and statistical uncertainty.
Finally, keep the wording matched to the evidence. “Consistent with GR” means the data and model agree within the test’s uncertainty. It does not mean GR has been proved universally, and a statistical tension alone does not mean it has been falsified.
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What does black-hole ringdown tell scientists?
Ringdown carries information about a newly formed black hole as it settles. In GR, the remnant’s mass and spin determine the expected frequencies and damping times of its quasi-normal modes, which scientists compare with the measured post-merger signal.
Can scientists test GR with only one ringdown harmonic?
Yes. A single harmonic can support a consistency check against remnant properties inferred from earlier portions of the event. Resolving more than one harmonic enables a stronger, cross-mode test of whether the inferred properties fit one Kerr black hole.
Does a result consistent with GR prove the theory is correct?
No. It means the analyzed data do not require a departure from GR at the sensitivity and under the assumptions of that test. It does not rule out every alternative theory or establish that GR applies in every setting.
Have ringdown searches found evidence for echoes?
The GWTC-4.0 remnant paper reports no evidence for echoes in the events it analyzed. A non-detection constrains possibilities only within that search’s sensitivity and assumptions; it does not exclude every model that might produce echoes.
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The Bottom Line
Scientists test GR by comparing a remnant black hole’s measured ringdown frequencies and damping times with predictions based on its mass and spin, and by checking whether estimates from different phases or modes agree. Multiple resolved modes offer a direct no-hair test, but many signals are too short or weak for that comparison. Results to date are described as consistent with GR within the limits of the analyses—not as proof that no deviations are possible.
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