Hybrid Stars and Twin Configurations: Phase-Transition Densities Tested Against the Density and Shear Bounds

A strong first-order transition from hadronic to quark matter inside a neutron star can produce hybrid stars, and in some models a second, disconnected family of twin stars with the same mass but smaller radii. This paper tests the transition region, two to five times saturation density, against every branch of the density bound that could apply to it, and against the critical shear. At three times saturation the fractions attained are 8.64e-41 of the neutron branch, 1.58e-35 of the up-quark branch and 3.45e-36 of the down-quark branch. The critical shear on the neutron branch is 8.559e+32 per second, far above any shear a transition layer sustains. Phase transitions therefore reshape compact stars entirely through their own latent densities and pressures; no branch of the bound participates in creating, stabilising or destroying twin configurations. Simulated from stated assumptions, not measured.