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

Hawking’s area theorem states that the total event-horizon area of classical black holes (BHs) can never decrease. Existing gravitational-wave tests analyze single loud events (GW150914, GW230814, GW250114) and therefore certify the law only for the specific mergers observed. Here we perform the {\it first} population-level test, exploiting the recent decomposition of the GWTC-5 BBHs into a low-spin subpopulation of stellar-collapse origin and a high-spin subpopulation formed through hierarchical mergers of the former. If the high-spin BHs are merger remnants (i.e., second-generation BHs), the area law requires their horizon areas to statistically exceed the total pre-merger areas of the low-spin binaries. Using inspiral-only parameter estimation for 241 events, independent of merger-ringdown modeling, we find that both peaks in the horizon-area distribution of second-generation BHs lie above their first-generation counterparts, with probabilities of $0.9995$ ($3.3\sigma$) and $0.983$ ($2.1\sigma$), respectively. The area law thus holds statistically for the quasicircular, moderately spinning mergers that dominate current catalogs, which in turn underpins the robustness of our classification of stellar-collapse and hierarchical-merger BHs.