Numerical simulation of type II primordial black hole formation

This study investigates the formation of primordial black holes (PBHs) resulting from extremely large amplitudes of initial fluctuations in a radiation-dominated universe. We find that, for a sufficiently large initial amplitude, the configuration of trapping horizons shows characteristic structure due to the existence of bifurcating trapping horizons. We call this structure of the trapping horizons ``Type II PBH'', while the structure without a bifurcating trapping horizon ``Type I PBH'', which is typically generated from a relatively small amplitude of the initial fluctuation. In Ref.[1], in the dust-dominated universe, the Type II PBH can be realized by the Type II initial fluctuation, which is characterized by a non-monotonic areal radius as a function of the radial coordinate (throat structure) in contrast with the standard case with a monotonic areal radius (Type I fluctuation). Our research reveals that a type II fluctuation does not necessarily result in a type II PBH in the case of the radiation fluid. We also find that for the initial amplitude well above the threshold value, the resulting PBH mass may either increase or decrease with the initial amplitude depending on its specific profile rather than its fluctuation type.