Researchers have derived the local structure of the first common apparent horizon that emerges during the merger of two binary black holes. This event, occurring in a highly nonlinear regime, beyond the scope of post-Newtonian theories or perturbations of stationary black holes, has been shown to possess a universal description. The study reveals that the stability operator of the marginally outer trapped surface (MOTS) loses its invertibility at the moment of horizon formation, implying that the vanishing eigenvalue is the principal one and its eigenfunction is strictly positive. This theoretical framework allows for precise prediction of the horizon's geometry at the instant of its appearance.

Using Lyapunov-Schmidt reduction, it has been shown that branch separation follows a square-root law with a shared linear drift, translating into a tilted parabola up to linear order in time. The common horizon lies on a smooth MOTS tube tangent to the formation slice. Nearby temporal slices intersect this tube in outer and inner branches, whose separation scales as (t-t*)¹/². Horizon quantities with a nonzero first response along the zero mode inherit this square-root separation and a shared linear term.

These theoretical predictions have been rigorously tested in three numerical simulations of binary black hole mergers, including an eccentric, precessing, unequal-mass system. In all cases, both the worldtube geometry and quasilocal scalars followed the predicted scaling. With the next-order term included, free-exponent fits to the surface geometry and quasilocal functionals recovered 1/2 to within half a percent, and diagnostics agreed on the formation time within 5×10⁻⁵M. The observed correlation between horizon shear and gravitational-wave news suggests that common horizon formation could have a detectable signature in a short segment of the merger waveform.