Recent developments on kaon condensation and its astrophysical implications

We discuss three different ways to arrive at kaon condensation at n c ≃ 3 n 0 where n 0 is nuclear matter density: (1) Fluctuating around the n = 0 vacuum in chiral perturbation theory, (2) fluctuating around n V M near the chiral restoration density n χ where the vector manifestation of hidden local symmetry is reached and (3) fluctuating around the Fermi liquid fixed point at ∼ n 0 . They all share one common theoretical basis, “hidden local symmetry”. We argue that when the critical density n c < n χ 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 ≃ 1.5 M ⊙ . 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.