Fast-spinning massive black holes from slowly rotating low-metallicity stars: Implications for GW231123
The origin of massive black holes in the early universe remains uncertain and still unexplored. Pop III stars are among the first stellar sources capable of producing such remnants, but their evolution is very sensitive to rotation. We explore how slow initial rotation influences the evolution and black hole formation of very massive Pop III stars, and assess their potential to become massive, fast-spinning black holes consistent with GW events such as GW231123. We compute a grid of non-rotating and slowly rotating Pop III stellar models with initial masses of 80, 85, and 90 $M_\odot$ using the GENEC code. Our models include rotationally induced mixing and angular-momentum transport by magnetic torques. We analyse the CO core masses and their volume-averaged adiabatic index to assess stability against electron-positron pair creation. From the angular-momentum profiles at the end of He burning, we estimate the resulting black hole masses and dimensionless spins under the assumption of direct collapse. Our non-rotating and slowly rotating 80 and 85 $M_\odot$ models develop carbon-oxygen core masses between 31 and 36 $M_\odot$ and have an adiabatic index that remains above 4/3. Our models thus predict that Pop III stars can keep most of their mass and collapse directly to form black holes of 80 to 85 $M_\odot$ with dimensionless spins up to $a_{\rm BH} \lesssim 0.7$. Initially slowly rotating, massive Pop III stars can form very massive, rapidly spinning black holes just below the pair-instability regime. This supports interpreting the lower boundary of the PISN mass gap as a smooth, structure-dependent transition and identifies single-star Pop III evolution as a possible channel for massive fast-spinning black holes observed by gravitational-wave detectors, subject to the uncertain efficiency of internal angular-momentum transport and mass-loss prescriptions.