Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars

A previous investigation by one of the authors showed that the critical mass of a constant-density neutron star can become greater than eight solar masses under conditions of neutron condensation to form a separate phase of composite bosons, provided the scattering length of the bosons was on the order of a picometer. That analysis employed Newtonian gravity, but general relativity provides a more fundamental analysis. Using general relativity, a Klein-Gordon Lagrangian density with Gross-Pitaevskii term for the bosons, and an effective-field approximation for neutrons, we have determined the equilibrium states of a collapsed star in a spherically symmetric variable-density single phase comprising a ground-state boson condensate and degenerate gas of noninteracting neutrons. Our calculations show that boson scattering lengths of about 20 picometers can prevent collapse to stellar black holes.