Neutron, quark, and proto-neutron stars at the onset of formation of black-holes: the memory effect

Context. In previous papers it was shown that the function Γ(M,EOS) ≡ [αβ]GR/Λ0.8(R) is invariant (≈0.40) for pre main-sequence stars (PMS), white dwarfs (WD), and for neutron stars (NS) computed with equations of state using relativistic mean-field nucleon interactions. The form-factors αGR and βGR are related to the relativistic gravitational potential energy and the moment of inertia and are a key to handling the Jacobi virial equation, which is a powerful tool for investigating the stellar internal structure and evolution. We also found that Γ(M,EOS) is invariant for gaseous planets. Moreover, a macroscopic criterion of stability for NS was derived.