PBH abundance from delayed vacuum decay follows f_pbh ≈ M exp(-Q exp(-S3(Tp)/Tp)), so S3(Tp)/Tp super-exponentially controls how many black holes form.
Revisiting formation of primordial black holes in a supercooled first- order phase transition,
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Super-exponential Primordial Black Hole Production via Delayed Vacuum Decay
PBH abundance from delayed vacuum decay follows f_pbh ≈ M exp(-Q exp(-S3(Tp)/Tp)), so S3(Tp)/Tp super-exponentially controls how many black holes form.