Antikaon condensation in neutron stars

We investigate the condensation of charged $K^-$ meson and neutral $\bar K^0$ meson in dense neutron star matter. Calculations are performed in relativistic mean field models in which both the baryon-baryon and (anti)kaon-baryon interactions are mediated by meson exchange. It is found that $\bar K^0$ condensation is quite sensitive to the antikaon optical potential and depends more strongly on the nucleonic equation of state. For moderate values of antikaon potential and a rather stiff equation of state, a significant region of maximum mass star will contain $\bar K^0$ meson. The critical density of $\bar K^0$ condensation is always higher than that of $K^-$ condensation. With the appearance of $K^-$ and $\bar K^0$ condensates, pairs of $p-K^-$ and $n-\bar K^0$ are produced with equal proportion leading to a perfectly symmetric matter of nucleons and antikaons in neutron stars. Along with $K^-$ condensate, $\bar K^0$ condensate makes the equation of state much softer resulting in smaller maximum mass stars compared to the case without any condensate.