New criterion for direct black hole formation in rapidly rotating stellar collapse

We study gravitational collapse of rapidly rotating relativistic polytropes of adiabatic indices Γ=1.5 and 2. The nondimensional spin parameter of the system q≡J/M2 where J and M are the total angular momentum and the gravitational mass is set to be larger than unity. First, analyzing initial distributions of mass and spin parameters inside the stars, we predict the final outcome after the collapse proposing a new criterion for direct black hole formation as qc<1 where qc denotes an effective spin parameter of the stellar central region. To confirm our predictions, we then perform fully general relativistic simulations assuming axial and equatorial symmetries. It is found that in contrast with previous conclusions for the criterion of no black hole formation, a black hole is formed even from a star with q>1 if the condition qc<1 is satisfied. For qc<1, a seed black hole is always formed first, and then, it grows as the ambient fluid elements accrete onto it. We also find that the time evolution of the relation between angular momentum and mass enclosed in the seed black hole can be approximately determined from the initial profiles of the density and the specific angular momentum