Nonlinear simulations show neighboring curvature peaks can merge or split into multiple primordial black holes instead of isolated collapses

Albert Escrivà and collaborators ran 3+1 numerical-relativity simulations tracking the evolution of bimodal primordial curvature perturbations. They tracked apparent horizons and introduced a nonspherical compaction diagnostic based on Hawking mass referenced to equal-area FLRW spheres. This diagnostic peaks at K_form,c ≈ 0.56 as an empirical threshold for PBH formation, with profile-dependent scatter. The work shows that maximum curvature amplitude is insufficient; the competition between local and enclosing compaction branches decides single versus double collapse outcomes.

Standard PBH calculations assume rare peaks act as isolated regions. These simulations reveal three possible fates for neighboring perturbations: dispersion, collective merger into one PBH, or distinct local collapses yielding two PBHs identified by disconnected apparent horizons. The signed linear surface strength on probing spheres further discriminates outcomes for bimodal cases. This directly challenges the one-to-one mapping used in most PBH abundance forecasts.

The findings connect to dark-matter and gravitational-wave constraints because clustered PBH formation alters merger rates and spatial distributions. Earlier analytic and spherical-collapse models missed these collective effects. Future work needs larger simulation suites spanning realistic power spectra to quantify the fraction of multi-PBH events.

Observational tests could come from pulsar-timing arrays or LIGO-Virgo-KAGRA stochastic backgrounds once formation-rate predictions incorporate the new thresholds. Higher-resolution runs with varied initial separations would tighten the empirical K_form criterion.