Numerical simulations of primordial black hole formation via delayed first-order phase transitions

We perform fully nonlinear, spherically symmetric numerical simulations of superhorizon false-vacuum-domain (FVD) collapse in a coupled gravity-scalar-fluid system to study primordial black hole (PBH) formation during delayed first-order phase transitions (FOPTs). Using adaptive mesh refinement to resolve the bubble wall, we identify three dynamical outcomes: type B (supercritical) PBHs with an interior baby universe and a bifurcating trapping horizon, type A (subcritical) PBHs with an apparent horizon formed by direct wall collapse, and dispersal with no PBH formation. To separate these three cases, we evaluate two commonly used PBH-formation criteria: the time scale ratio $t_\mathrm{H}/t_\mathrm{V}$ (horizon crossing time versus vacuum-energy domination time) and the local density contrast $\delta(t_\mathrm{H})$ at horizon crossing. For the parameter space explored, we find that $t_\mathrm{H}/t_\mathrm{V}$ is a more robust predictor of outcome: type B PBHs form when $t_\mathrm{H}/t_\mathrm{V} \gtrsim 1$ (critical range $\sim 1.1 - 1.6$ in our survey), type A PBHs arise when $t_\mathrm{H}/t_\mathrm{V}$ is below this threshold but remains above a lower bound (typical range $\sim 0.35 - 0.7$), and no-PBH dispersal occurs when $t_\mathrm{H}/t_\mathrm{V}$ falls below this lower bound. When a clear thin-wall FVD boundary exists, $\delta(t_\mathrm{H})$ can correspondingly distinguish different outcomes (roughly $\delta_c(t_\mathrm{H}) \sim 1 - 1.7$ for type B and $\delta_c(t_\mathrm{H}) \sim 0.35 - 0.5$ for type A), but is highly sensitive to wall structure and model details and thus less universal. These results offer new insights into the dynamics of FVD collapse, quantify practical PBH-formation thresholds, and pave the way for precise predictions of PBH abundance from delayed FOPTs.