The Rotation-Displaced Bounce: How Far Below the Aldred Limit a Spinning Core Turns Around

The Aldred Limit density rho_A = 9.72e+54 g per cubic centimetre is the turnaround density of a non-rotating collapse. Real cores rotate, and rotation supplies part of the support against gravity, so a spinning core should turn around below the Limit. This paper computes the displacement for cores of 1.4 to 25 solar masses with specific angular momenta from 1e15 to 1e18 square centimetres per second, the stated range for stellar cores. The rotational energy density at the bounce radius is converted to an equivalent density and expressed as a fraction of the support the spin-torsion term must provide. The displacement is minute across most of the range: as small as 99.999900 percent for a slowly rotating light core, and at most 99.9999 percent for the most extreme combination tabulated, where the equatorial speed at the bounce radius reaches 815671798255.005 of the speed of light. The bounce radius of a 1.4 solar mass core at the Limit is 0.0 m. The plain conclusion is that rotation displaces the bounce only slightly: the Limit is, to better than a tenth of a percent except in near-breakup cases, the turnaround density of spinning cores as well. Computed from stated assumptions, not measured.