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We investigate the possibility of a supernova in supermassive ($5 \times 10^4\;M_\odot$) population III stars induced by a general relativistic instabilityoccurring in the helium burning phase. This explosion could occur via rapidhelium burning during an early contraction of the isentropic core. Such anexplosion would be visible to future telescopes and could disrupt the proposeddirect collapse formation channel for early universe supermassive black holes.We simulate first the stellar evolution from hydrogen burning using a 1Dstellar evolution code with a post Newtonian approximation; at the point ofdynamical collapse, we switch to a 1D (general relativistic) hydrodynamics codewith the Misner-Sharpe metric. In opposition to a previous study, we do notfind an explosion in the non rotating case, although our model is close toexploding for a similar mass to the explosion in the previous study. When weinclude slow rotation, we find one exploding model, and we conclude that therelikely exist additional exploding models, though they may be rare.

The Final Fate of Supermassive $M \sim 5 \times 10^4 \; M_\odot$ Pop III Stars: Explosion or Collapse?