The final fate of supermassive M ∼ 5 × 104 M⊙ Pop III stars: explosion or collapse?

We investigate the possibility of a supernova in supermassive ($5 \times 10^4 \;M_\odot$) population III stars induced by a general relativistic instability occurring in the helium burning phase. This explosion could occur via rapid helium burning during an early contraction of the isentropic core. Such an explosion would be visible to future telescopes and could disrupt the proposed direct collapse formation channel for early universe supermassive black holes. We simulate first the stellar evolution from hydrogen burning using a 1D stellar evolution code with a post Newtonian approximation; at the point of dynamical collapse, we switch to a 1D (general relativistic) hydrodynamics code with the Misner-Sharpe metric. In opposition to a previous study, we do not find an explosion in the non rotating case, although our model is close to exploding for a similar mass to the explosion in the previous study. When we include slow rotation, we find one exploding model, and we conclude that there likely exist additional exploding models, though they may be rare.