Recent Developments on Kaon Condensation and Its Astrophysical Implications

We discuss three different ways to arrive at kaon condensation at nc ≃ 3n0 where n0 is nuclear matter density: (1) Fluctuating around the n = 0 vacuum in chiral perturbation theory, (2) fluctuating around nVM near the chiral restoration density nχ where the vector manifestation of hidden local symmetry is reached and (3) fluctuating around the Fermi liquid fixed point at ∼ n0. They all share one common theoretical basis, “hidden local symmetry.” We argue that when the critical density nc < nχ is reached in a neutron star, the electrons turn into K − mesons, which go into an S-wave Bose condensate. This reduces the pressure substantially and the neutron star goes into a black hole. Next we develop the argument that the collapse of a neutron star into a black hole takes place for a star of M ≃ 1.5M⊙. This means that Supernova 1987A had a black hole as result. We also show that two neutron stars in a binary have to be within 4% of each other in mass, for neutron stars sufficiently massive that they escape helium shell burning. For those that are so light that they do have helium shell burning, after a small correction for this they must be within 4% of each other in mass. Observations support the proximity in mass inside of a neutron star binary. The result of strangeness condensation is that there are ∼ 5 times more low-mass black-hole, neutron-star binaries than double neutron-star binaries although the former are difficult to observe. Preprint submitted to Physics Reports 29 February 2008