Verification of the Black Hole Area Law with GW230814 (2509.03480v1)

Abstract: We present observational confirmation of Hawking's black-hole area theorem using the newly released gravitational-wave data from the GWTC-4 catalog. We have analyzed two high signal-to-noise ratio binary black hole (BBH) merger events, including GW230814 and GW231226, from the first part of the LIGO-Virgo-KAGRA O4 run, and measured the (total) horizon area of the black holes before and after merger. For both events, the horizon area of the remnant black hole is found to be greater than the total horizon area of the two pre-merger black holes at a high possibility (effectively $\gtrsim 99\%$), and particularly with GW230814 we have a significance level of $\gtrsim 5\sigma$ for the {\it first} time. These results provide the direct convincing verification of the black-hole area law, further bolstering the validity of classical general relativity in the dynamical, strong-field regime.

• The paper presents a robust confirmation of Hawking's black hole area law with >5.5σ significance for GW230814 using advanced Bayesian inference on gravitational wave data.
• The methodology employs a gating-and-inpainting procedure and state-of-the-art waveform models from PyCBC and LALSuite to separate inspiral and merger-ringdown phases for accurate parameter estimation.
• The findings validate classical general relativity in the strong-field regime and set a benchmark for future tests with next-generation detectors.

Verification of the Black Hole Area Law with GW230814

Introduction

This paper presents a high-confidence observational test of Hawking's black-hole area theorem using gravitational-wave data from the GWTC-4 catalog, specifically focusing on two high-SNR binary black hole (BBH) merger events: GW230814 and GW231226. The area theorem, a fundamental result in classical general relativity, asserts that the total event-horizon area of a system of black holes cannot decrease over time. Previous tests, such as those using GW150914, achieved moderate confidence levels ($\sim 2-3\sigma$), but the improved sensitivity and data quality of the O4 run now enable a much more stringent verification.

Methodology

The analysis employs a "gating-and-inpainting" procedure to isolate the inspiral (pre-merger) and merger-ringdown (post-merger) phases of the GW signal. Bayesian inference is performed using the Bilby library and Dynesty nested sampling, with waveform generation and data handling managed by PyCBC and LALSuite. The inspiral analysis reconstructs the component masses and spins of the progenitor black holes, while the merger-ringdown analysis infers the remnant's mass and spin. The horizon area for a Kerr black hole is computed as:

$$A = 4\pi m^2 \left( 1 + \sqrt{1 - \chi^2} \right)^2$$

where $m$ is the mass and $\chi$ is the dimensionless spin. The total initial area $A_{\rm i}$ is the sum of the areas of the two progenitors, and the final area $A_{\rm f}$ is that of the remnant. The ratio

$$\mathcal{R} = \frac{A_{\rm f}-A_{\rm i}}{A_{\rm f,e}-A_{\rm i}}$$

compares the measured change in area to the GR prediction.

Results

Posterior distributions for the remnant mass and spin, inferred independently from inspiral and merger-ringdown analyses, are consistent with each other and with full IMR analyses.

Figure 1: Posterior distributions for the redshifted remnant mass $M_{\rm f}$ and dimensionless spin $\chi_{\rm f}$ for GW230814 (left) and GW231226 (right), inferred from inspiral-only and merger-ringdown analyses.

Robustness checks confirm that varying the inspiral gate-start time and waveform family has negligible impact on the inferred parameters.

Figure 2: Posterior distributions for component masses and spins for GW230814 (left) and GW231226 (right), obtained using IMRPhenomXPHM waveform model with different $\delta t$.

Figure 3: Posterior distributions for component masses and spins for GW230814 (left) and GW231226 (right) with different waveform models obtained in pre-merger analyses ($\delta t=0$).

The area law test yields overwhelming evidence for an increase in total horizon area in both events. For GW230814, the probability of a decrease in area is $p(\mathcal{R}<0)=0.0002\%$ (XPHM), corresponding to a significance of $>5.5\sigma$. For GW231226, the probability is $1.14\%$ (XPHM), or $0.71\%$ (XO4a), corresponding to $\sim 2.5\sigma$.

Figure 4: Probability distribution of the ratio $\mathcal{R}$ of the measured and expected change in black hole horizon area for GW230814 and GW231226. Distributions lie almost entirely to the right of $R=0$, confirming the area law.

Ringdown-only analyses, using the dominant $220$ quasinormal mode, show no significant evidence for additional modes in either event, in contrast to previous findings for GW231123.

Figure 5: Bayes factors for models including an extra ringdown mode versus the single-mode (220) model, as a function of the chosen ringdown start time, for GW230814 (left) and GW231226 (right).

Implications and Future Directions

The results provide a direct and statistically robust confirmation of Hawking's area theorem in the dynamical, strong-field regime of general relativity. The $>5.5\sigma$ significance for GW230814 marks a substantial improvement over previous tests, which were limited by data quality and SNR. The methodology demonstrates the increasing power of GW observations to probe fundamental aspects of gravity, with systematic uncertainties from waveform modeling and segmentation timing shown to be negligible at current precision.

As detector sensitivity improves and more high-SNR BBH mergers are observed, population-level studies will become feasible, enabling the search for outlier events that might signal new physics (e.g., exotic compact objects or beyond-GR effects). Next-generation detectors such as the Einstein Telescope and Cosmic Explorer will further enhance the precision of area-law tests and may be sensitive to minute deviations from classical predictions, potentially probing quantum gravitational effects.

Conclusion

This paper achieves the first $>5\sigma$ observational confirmation of the black-hole area law using GW230814, with GW231226 providing additional support at lower significance. The findings reinforce the validity of classical general relativity in the strong-field regime and establish a new benchmark for experimental tests of black hole thermodynamics. Future GW observations will enable even more stringent tests and may open avenues for detecting new physics in the merger dynamics of compact objects.