Horizon Formation in Stellar Collapse Occurs at Densities Far Below the Density Bound

Whether a density bound can prevent black hole formation in stellar collapse depends on a race: the collapsing matter must reach the bound before its radius falls inside its Schwarzschild radius. This paper computes the density of a collapsing mass at the moment of horizon formation, rho_H = 3 c^6 / (32 pi G^3 M^2), for progenitors from 3 to 100 solar masses, and finds the mass at which the race would be tied. At 10 solar masses the horizon forms at 1.84e+17 kg per cubic metre, a fraction 1.90e-41 of the neutron-branch bound; at 3 solar masses it forms at 2.05e+18 kg per cubic metre. The tie occurs at a mass of 8.659e+10 kg, or 4.35e-20 solar masses. For every stellar mass, the horizon wins the race by an enormous margin, and any turnaround at the bound occurs inside the horizon. This is a negative result, stated plainly. Simulated, not measured.