image: Probability density distributions of the ratio between the measured and expected changes in the horizon area of the merged black hole. The results compare two post‑merger modelling approaches: the “pIMR” model, which uses the post‑merger portion of an inspiral‑merger‑ringdown waveform, and the “QNM” model, which represents the ringdown as a superposition of quasinormal modes of a perturbed Kerr black hole. The analysis also examines different ringdown start times t>, set at 4 or 6 times tMf (0.309 ms) after the reference strain peak. The grey‑shaded region indicates cases where the final horizon area is smaller than the sum of the initial two. The vertical dashed line at 1 corresponds to the prediction of general relativity.
Credit: ©Science China Press
A research team at the Purple Mountain Observatory (PMO) announces a significant observational test of the black-hole “area law” using the gravitational-wave event GW230814. In 1971, physicist Stephen Hawking proposed that for classical black holes the total area of their event horizons cannot decrease over time. The merger of two black holes offers one of the few accessible ways to test this prediction — but accurately measuring the masses and spins (and hence the horizon areas) of the progenitor and resultant black holes has proved extremely challenging.
The PMO team turned to the high signal-to-noise ratio event GW230814, drawn from the fourth gravitational-wave transient catalog. Black-hole coalescence can be broadly divided into three phases: inspiral (two black holes spiraling inward), merger (the highly nonlinear coalescence), and ringdown (the newly formed black hole relaxing). The merger phase is the most dynamic and potentially most susceptible to deviations from general relativity; by contrast, the inspiral and ringdown phases lie in regimes where general relativity is typically a reliable approximation.
Recognising this, the authors performed independent parameter inference on the inspiral phase and the ringdown phase of GW230814, deriving constraints on the masses and spins of the two original black holes and the final merged black hole — and from those, the horizon areas. Across their analysis they carefully accounted for key uncertainties including sky-location error, waveform-template systematic effects, choice of ringdown modelling, and the time boundaries for inspiral end and ringdown start.
The analysis shows that, after considering these uncertainties, the posterior probability that the final black hole’s horizon area exceeds the sum of the progenitors’ horizon areas is extremely high. The one-sided statistical significance can reach about 4.1σ. This finding strongly supports the black-hole area law, and further corroborates the self-consistency and validity of general relativity in the strong-field, dynamical regime of black-hole mergers.
This independent verification of Hawking’s area law not only reinforces a foundational prediction of black-hole physics, but also strengthens confidence in our understanding of gravitational dynamics under the most extreme conditions. Moreover, the study provides a solid basis for future investigations into black-hole thermodynamics, quantum-gravity corrections and even more stringent tests of gravitational theory in the most extreme astrophysical environments.