Population-Level Verification of the Black-Hole Area Law with First- and Second-Generation Black Holes

Abstract

Hawking's area theorem states that the total event-horizon area of classical black holes can never decrease. Gravitational-wave tests of this law have so far focused on individual loud mergers, thus probing only a sparse subset of binary parameter space. Here we perform the \emph{first} population-level test. We exploit the decomposition of the coalescing black holes in the latest gravitational-wave catalogue into a low-spin subpopulation of stellar-collapse origin and a high-spin subpopulation assembled through hierarchical mergers of the former. If the high-spin black holes are merger remnants, the area theorem requires their horizon areas to exceed the total pre-merger areas of the low-spin binaries. Using parameter estimation restricted to the inspiral of 241 events, so that no merger-ringdown information enters the inference, we find that both peaks of the horizon-area distribution of second-generation black holes lie above their first-generation counterparts. The displacement is significant at each peak ($2.1$--$3.7\sigma$), and when we tie the two subpopulations with a single common shift, an area decrease is excluded decisively ($\gtrsim5.0\sigma$). The second law of black-hole mechanics thus holds statistically across the quasicircular, moderately spinning mergers that dominate current catalogues, which in turn underpins the robustness of our classification of stellar-collapse and hierarchical-merger black holes.