Black Hole Spectroscopy and Tests of General Relativity with GW250114 (2509.08099v1)

Abstract: The binary black hole signal GW250114, the loudest gravitational wave detected to date, offers a unique opportunity to test Einstein's general relativity (GR) in the high-velocity, strong-gravity regime and probe whether the remnant conforms to the Kerr metric. Upon perturbation, black holes emit a spectrum of damped sinusoids with specific, complex frequencies. Our analysis of the post-merger signal shows that at least two quasi-normal modes are required to explain the data, with the most damped remaining statistically significant for about one cycle. We probe the remnant's Kerr nature by constraining the spectroscopic pattern of the dominant quadrupolar ($\ell = m = 2$) mode and its first overtone to match the Kerr prediction to tens of percent at multiple post-peak times. The measured mode amplitudes and phases agree with a numerical-relativity simulation having parameters close to GW250114. By fitting a parameterized waveform that incorporates the full inspiral-merger-ringdown sequence, we constrain the fundamental $(\ell=m=4)$ mode to tens of percent and bound the quadrupolar frequency to within a few percent of the GR prediction. We perform a suite of tests -- spanning inspiral, merger, and ringdown -- finding constraints that are comparable to, and in some cases 2-3 times more stringent than those obtained by combining dozens of events in the fourth Gravitational-Wave Transient Catalog. These results constitute the most stringent single-event verification of GR and the Kerr nature of black holes to date, and outline the power of black-hole spectroscopy for future gravitational-wave observations.

• The paper leverages GW250114's high signal-to-noise ratio to precisely identify multiple quasi-normal modes, rigorously testing general relativity and confirming the Kerr metric.
• It employs both agnostic and Kerr-constrained ringdown models to yield QNM frequency and damping time constraints that are up to twice as stringent as previous multi-event analyses.
• The study validates the Hawking area theorem and inspiral phase consistency through full IMR analysis, showcasing a scalable methodology for future precision GR tests.

Black Hole Spectroscopy and General Relativity Tests with GW250114

Overview and Context

The detection of GW250114, the highest signal-to-noise ratio (SNR) gravitational wave event to date, provides an exceptional opportunity to probe the strong-field, high-velocity regime of general relativity (GR) and to test the Kerr nature of black holes via black hole spectroscopy. This work leverages the unprecedented SNR of GW250114 to perform a suite of precision tests spanning the inspiral, merger, and ringdown phases, utilizing both agnostic and Kerr-informed models, and comparing results to numerical relativity (NR) simulations. The analysis yields constraints on GR and the Kerr metric that are comparable to, and in several cases more stringent than, those obtained by combining dozens of previous events.

Methodology

Signal Characterization and Modeling

The GW250114 event is modeled as a quasi-circular, spin-precessing binary black hole (BBH) merger, with component masses $33.6^{+1.2}_{-0.9} M_\odot$ and $32.2^{+1.3}_{-1.1} M_\odot$, and low dimensionless spins ($\leq 0.24$, $\leq 0.26$). The eccentricity is tightly constrained ($e \leq 0.03$). The analysis employs the NRSur7dq4 model for the full inspiral-merger-ringdown (IMR) waveform, and multiple ringdown models (ringdown, pyRing, QNMRF) for post-merger spectroscopy.

Black Hole Spectroscopy

The post-merger signal is analyzed as a superposition of exponentially damped sinusoids (quasi-normal modes, QNMs), with complex frequencies determined by the remnant's mass and spin. Fits are performed for the dominant quadrupolar mode (220), its first overtone (221), and the hexadecapolar mode (440). Both agnostic (free frequency/damping) and Kerr-constrained models are used, with fits initiated at various post-peak times to probe the validity regime of linear perturbation theory.

Full-Signal Parametric Tests

The pSEOBNR framework is used to fit the entire IMR signal, introducing fractional deviations in QNM frequencies and damping times. This approach enables simultaneous constraints on multiple modes and enforces continuity across the waveform, leveraging NR-calibrated amplitude models.

Inspiral Phase Tests

Post-Newtonian (PN) phasing is tested using the FTI and TIGER pipelines, introducing deformation parameters at each PN order and performing principal component analysis (PCA) to probe correlated deviations. Constraints are compared to those from hierarchical analyses of previous catalogs.

Consistency and Area Theorem Tests

Remnant mass and spin are inferred independently from low- and high-frequency portions of the signal, and their consistency is quantified. The Hawking area theorem is tested by comparing the total initial and final horizon areas, with significance estimated via the IMR consistency test.

Key Results

Quasi-Normal Mode Identification

• At least two QNMs (220, 221) are required to explain the post-merger signal, with the 221 overtone remaining statistically significant for $\sim$1 cycle.
• The amplitudes and phases of the 220 and 221 modes are consistent with NR simulations of GW250114-like systems at $\geq 38\%$ credibility.
• The 440 mode is constrained for the first time, with its frequency bounded to tens of percent.

Kerr Metric and No-Hair Theorem Tests

• The spectroscopic pattern of the dominant and overtone modes matches the Kerr prediction to within tens of percent at multiple post-peak times.
• The 220 QNM frequency is constrained to within a few percent of the GR prediction: $\delta f_{220} = 0.02^{+0.02}_{-0.02}$, $\delta \tau_{220} = -0.01^{+0.10}_{-0.09}$.
• The 440 mode frequency deviation is $\delta f_{440} = -0.06^{+0.25}$, with the damping time weakly constrained.
• These bounds are approximately twice as stringent as those obtained by combining 17 events in GWTC-4.0.

Inspiral Phase Constraints

• FTI analysis yields $|\delta \phi_0| = 0.00^{+0.03}$ and $|\delta \phi_3| = -0.01^{+0.03}$, 2-3 times more stringent than joint GWTC-4.0 constraints.
• PCA identifies the leading component as $\delta \phi_{\text{PCA}} = -0.01^{+0.02}_{-0.02}$, consistent with GR.

Remnant Consistency and Area Theorem

• Remnant mass and spin inferred from different signal portions are consistent: $\Delta M_f/M_f = 0.02^{+0.07}$, $\Delta \chi_f/\chi_f = -0.01^{+0.11}$.
• The Hawking area theorem is verified at $4.80\sigma$ credibility, with the final area exceeding the sum of initial areas.

Residuals and Systematics

• No statistically significant residual coherent power is found after subtracting the best-fit waveform; the residual network SNR is $6.86$ (p-value $0.34$).
• The fitting factor is $0.996$, indicating excellent agreement between the model and data.

Implications

Theoretical

The results provide the most stringent single-event verification of GR and the Kerr nature of black holes to date. The consistency of multiple QNMs with Kerr predictions supports the no-hair theorem and the uniqueness of the Kerr solution in astrophysical settings. The constraints on QNM frequencies and damping times can be mapped to bounds on alternative gravity theories (e.g., dynamical Chern-Simons gravity, $V_{\text{dCS}} < 32.2$ km for axial perturbations), and on exotic compact objects.

Practical

The demonstrated ability to perform black hole spectroscopy with a single high-SNR event highlights the scientific potential of future gravitational wave observations. The methodology enables precision tests of GR, the Kerr metric, and the area theorem, and can be extended to probe higher-order modes, overtones, and correlated deviations in the PN regime. The analysis framework is robust to modeling uncertainties and instrumental systematics, and is scalable to larger event catalogs.

Future Directions

• Improved detector sensitivity and increased event rates will enable routine multi-mode spectroscopy and more stringent tests of GR.
• Extension of amplitude models to include overtones and non-quasi-circular orbits will enhance the fidelity of ringdown analyses.
• Direct Bayesian analyses using waveform predictions from alternative gravity theories will yield more robust constraints.
• Systematic studies of selection effects, noise non-stationarity, and astrophysical priors are needed to refine catalog-level tests.

Conclusion

The analysis of GW250114 establishes new benchmarks for precision tests of general relativity and black hole spectroscopy. The event enables identification and constraint of multiple QNMs, verification of the Kerr metric, and validation of the Hawking area theorem, with bounds that surpass those from previous catalog-level analyses. The methodologies and results presented here will inform future gravitational wave science, providing a template for exploiting high-SNR events in the strong-field regime.