Black hole mass spectrum as a function of the CO core mass for different PPISN prescriptions. Solid blue line: this work, non-rotating progenitors at [Fe/H] =−3; dash-dotted orange line: F19 PPISN threshold ($M_{\mathrm{CO}}^{\mathrm{PPISN}}=41{\mathrm{M}}_{\odot }$) applied to the S17 pre-SN progenitors; dotted green line: W17 PPISN threshold ($M_{\mathrm{CO}}^{\mathrm{PPISN}}=28{\mathrm{M}}_{\odot }$) applied to the S17 pre-SN progenitors. Circles (crosses) represent the models that are stable (unstable) against pair production, and squares represent the first star exploding as PISNe.