Testing the no-hair theorem with GW150914 (1905.00869v2)

Abstract: We analyze gravitational-wave data from the first LIGO detection of a binary black-hole merger (GW150914) in search of the ringdown of the remnant black hole. Using observations beginning at the peak of the signal, we find evidence of the fundamental quasinormal mode and at least one overtone, both associated with the dominant angular mode ($\ell=m=2$), with $3.6\sigma$ confidence. A ringdown model including overtones allows us to measure the final mass and spin magnitude of the remnant exclusively from postinspiral data, obtaining an estimate in agreement with the values inferred from the full signal. The mass and spin values we measure from the ringdown agree with those obtained using solely the fundamental mode at a later time, but have smaller uncertainties. Agreement between the postinspiral measurements of mass and spin and those using the full waveform supports the hypothesis that the GW150914 merger produced a Kerr black hole, as predicted by general relativity, and provides a test of the no-hair theorem at the ${\sim}10\%$ level. An independent measurement of the frequency of the first overtone yields agreement with the no-hair hypothesis at the ${\sim 20}\%$ level. As the detector sensitivity improves and the detected population of black hole mergers grows, we can expect that using overtones will provide even stronger tests.

• The paper demonstrates that gravitational-wave ringdown analysis reveals at least one overtone with a 3.6σ confidence level, bolstering theoretical predictions.
• The paper accurately measures the remnant black hole's mass and spin solely from the ringdown phase, yielding estimates consistent with full-signal analyses.
• The paper reduces measurement uncertainties by incorporating overtones, enabling a robust test of the no-hair theorem at a precision level of about 20%.

Analyzing GW150914 to Test the No-Hair Theorem

The paper "Testing the no-hair theorem with GW150914," by Isi et al., explores gravitational-wave data from the landmark detection of a binary black-hole merger, focusing on the ringdown phase of the remnant black hole. This phase provides a unique opportunity to test the no-hair theorem within the framework of general relativity, which posits that a black hole can be fully characterized by its mass and spin.

Key Findings

1. Gravitational-Wave Analysis: The paper utilizes postinspiral data starting from the peak of the gravitational wave signal to isolate the fundamental quasinormal mode and its overtones. The analysis indicates evidence of at least one overtone with a confidence level of 3.6σ, supporting previous findings in the literature.
2. Mass and Spin Measurement: The authors obtain estimates for the remnant black hole's mass and spin exclusively from the ringdown data. These estimates exhibit compatibility with those derived from the complete waveform analysis, thereby corroborating the formation of a Kerr black hole as predicted by general relativity.
3. Improved Precision: The use of overtones allows for reduced uncertainties in the mass and spin measurements compared to those derived from only the fundamental mode. Specifically, the estimates differ from full-signal measurements by 7%, with a confidence interval extending to 10%.
4. Test of the No-Hair Theorem: This paper provides one of the first significant tests of the no-hair theorem using gravitational waves, validating it at a precision level of approximately 20%. This work thus contributes to the black-hole spectroscopy program aimed at characterizing black-hole remnants through their ringdown spectra.

Theoretical and Practical Implications

• Enhanced Black Hole Spectroscopy: Incorporating overtones into the analysis strengthens the testing framework for the no-hair theorem, suggesting a multimodal spectral analysis can reveal more intricate details about black-hole post-merger dynamics.
• Future Observations: As gravitational-wave detectors like LIGO and Virgo continue to enhance their sensitivity, utilizing overtones will be increasingly valuable, potentially leading to more stringent tests of general relativity and the discovery of deviations from the predicted Kerr black holes. This approach might also distinguish black-hole mimickers, should they exist.
• Refinement and Extensions: Future studies might focus on refining the understanding of overtone excitations and amplitudes based on binary properties. Enhanced modeling could reduce uncertainties and dimensionality in analyses, providing more robust predictions from general relativity.

In summary, this paper represents a sophisticated analysis of gravitational wave data to empirically test fundamental predictions of general relativity. Its methodology and findings are likely to have enduring impacts on the field of gravitational-wave astronomy and the paper of black hole physics.