The black hole - pair instability boundary for high stellar rotation

The Pair Instability (PI) boundary is crucial for understanding heavy merging Black Holes (BHs) and the second mass gap's role in galactic chemical evolution. So far, no works have critically and systematically examined how rotation and mass loss affect the PI boundary or BH masses below it. Rapid rotation significantly alters stellar structure and mass loss, which is expected to have significant effects on the evolution of stellar models. We have previously derived a critical core mass independent of stellar evolution parameters, finding the BH (Pulsational) PI boundary at $M_{ CO, crit} = 36.3 M_\odot$ for a carbon-oxygen (CO) core. Using MESA, we model massive stars around the PI boundary for varying rotation rates and metallicities. We implement mechanical mass loss in MESA, studying its effects on massive stars in low-metallicity environments. Below $1/100$th $Z_\odot$, mechanical mass loss dominates over radiative winds. We check the BH-PI boundary for rapid rotators to confirm our critical core mass criterion and derive model fits describing rotation's impact on core and final masses. Fast rotators reach a point (typically $\Omega / \Omega_{crit} \approx 0.6$) where the entire star becomes chemically homogeneous, evolving like a stripped star. This lowers the maximum BH mass before PI to its critical core mass of $M_{CO, crit} = 36.3 M_\odot$, aligning with the bump feature in the BH mass distribution observed by LIGO/VIRGO.