Verification of the Black Hole Area Law with GW230814

TL;DR

The paper tests Hawking's area theorem using the high-SNR BBH merger GW230814, by comparing the total horizon area before merger $A_i$ with the remnant area $A_f$ inferred from independent pre- and post-merger analyses. It uses a gating strategy to separate signal segments, analyzes multiple GR waveform models and a Kerr QNM ringdown framework, and defines the area ratio $\mathcal{R}=(A_f-A_i)/(A_f^*-A_i)$ against the GR-predicted change $A_f^*-A_i$. Across a range of gate placements and models, the study finds $P(\mathcal{R}<0)$ between $20\,\text{ppm}$ and $0.57\%$, corresponding to a $2.5$–$4.1\sigma$ confirmation that $A_f > A_i$ and thus support for the area theorem. The results are robust to sky-location uncertainties and modeling choices, demonstrating GR’s validity in dynamical, strong-field regimes and highlighting the potential for future, higher-SNR observations to tighten these tests.

Abstract

We present an observational confirmation of Hawking's black-hole area theorem using the newly released gravitational-wave data from the GWTC-4.0. We analyze the high signal-to-noise ratio binary black hole (BBH) merger GW230814 and measure the (total) horizon area of the black holes before and after the merger. For preferred (and reasonable) choices of the post-truncation start time, 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 (at least $\gtrsim 99.5\%$). Importantly, our analysis accounts for sky-location uncertainty. These results provide a stringent observational confirmation of the black-hole area law, further bolstering the validity of classical general relativity in the dynamical, strong-field regime.

Figures (6)

• Figure 1: Pre-merger posteriors for the (redshifted) component masses and spins of GW230814. Contours enclose $90\%$ credible regions. Left: comparison across waveform models at a fixed truncation $t_{<}=20\,t_{M}$. Right: dependence on the pre-truncation $t_{<}$ for XPHM.
• Figure 2: Post-merger posteriors for the (redshifted) remnant mass $M_{\rm f}$ and spin $\chi_{\rm f}$ of GW230814 from pIMR (left) and QNM (right) models. For reference, solid red contours show the reconstructed $M_{\rm f}$ and $\chi_{\rm f}$ from pre-merger analysis using XPHM and $t_{<}=20\,t_{M}$; dotted contours show the predictions from the full IMR analysis. Contours enclose $90\%$ credible regions. Crosses mark the maximum-likelihood points.
• Figure 3: Violin plots of the ratio $\mathcal{R}$ of the measured to the expected change in the black-hole horizon area for multiple combinations of $t_{<}$ and $t_{>}$, obtained with the pIMR analysis. The shaded gray regions indicate violation of the area law ($\mathcal{R}<0$); the red dashed lines ($\mathcal{R}=1$) mark the GR prediction.
• Figure 4: Probability distributions of the ratio $\mathcal{R}$ of the measured to the expected change in the black-hole horizon area for $t_{>}=4,6\,t_{M_{\rm f}}$ (both pIMR and QNM) with $t_{<}=20\,t_{M}$. The distributions lie almost entirely to the right of $\mathcal{R}=0$ (shaded gray), indicating that for these configurations the final horizon area exceeds the initial total area with high probability. The vertical line at $\mathcal{R}=1$ marks the GR prediction.
• Figure 5: Bayes factors for models including an extra QNM versus the single-mode (220) model, as a function of the chosen $t_{>}$ for GW230814.