Kaon condensation in neutron stars and high density behaviour of nuclear symmetry energy

We study the influence of a high density behaviour of the nuclear symmetry energy on a kaon condensation in neutron stars. We find that the symmetry e nergy typical for several realistic nuclear potentials, which decreases at high densities, inhibits kaon condensation for weaker kaon-nucleon coupling s at any density. There exists a threshold coupling above which the kaon co ndensate forms at densities exceeding some critical value. This is in contr ast to the case of rising symmetry energy, as e.g. for relativistic mean fi eld models, when the kaon condensate can form for any coupling at a suffici ently high density. Properties of the condensate are also different in both cases.