Threshold of primordial black hole formation in nonspherical collapse

We perform (3 + 1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal superhorizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for large amplitude of perturbations expected for PBH formation.