The Minimum Radius of a Bounced Core: Where the Aldred Limit Sits Against the Schwarzschild Radius

A mass that collapses to the Aldred Limit cannot be compressed further, so it has a minimum radius R_min = (3M/(4 pi rho_A))^(1/3). This paper computes that radius for masses from 0.1 to a million solar masses and compares it with the Schwarzschild radius of the same mass. For a 1.4 solar mass core the minimum radius is 0.0 m against a Schwarzschild radius of 4135 m, a ratio of 0.0000: the bounced core sits deep inside its own Schwarzschild radius. The ratio falls as M to the minus two-thirds, and the crossover mass at which the minimum radius equals the Schwarzschild radius is 4.355e-20 solar masses. Above that mass a collapsing object reaches its Schwarzschild radius before its density reaches the Limit, so the bounce, if it occurs, occurs inside a horizon; below it, no horizon forms before the bounce. The Limit therefore does not prevent black hole formation for stellar masses; it replaces the singularity inside with a bounced core of computable size. Computed from stated assumptions, not measured.