| In this work, we mainly investigate the properties of antikaon condensations, the relations between K condensations and the nucleons, hyperons and ? quartet, which are appeared in neutron star matter. Furthermore, the influence of antikaons on the neutron stars and their cooling history are studied too. The relativistic mean field theory (RMFT) of strong interaction is adopted in the first three parts, whereas the forth part includes both the model of weak interaction and the RMFT .Using RMFT , we study antikaon condensations in nucleons-only matter. Three parameter sets are adopted here, i.e., GL1, NL-SH and GPS250. The results show that K- and (K|—)0 condensations can be widely allowed for the optical potential of antikaons in the range of -120MeV—-160MeV. K- condensation always appears earlier than (K|—)0 condensation. K- condensation is chiefly responsible for the softening of the corresponding equation of state (EOS), which leads to a large reduction in the maximum masses of neutron stars. However, the chief role of (K|—)0 condensation is to make isospin saturated symmetric matter of antikaons and nucleons, respectively. Antikaon condensations are very sensitive to the EOS and the optical potential depth of antikaons. The deeper the optical potential of antikaons, the lower the critical densities of antikaon condensations. A lower mass neutron star and its bigger corresponding radius corresponds to a deeper optical potential of antikaons. It is also found that a stiff EOS favors antikaon condensations.Hyperons are considered in the system, so the hadron phase includes all of the baryon octet. The results show that the critical densities of K- mesons are higher than the case for nucleons-only matter, whereas (K|—)0 condensation is insensitive to hyperons. With the inclusion of hyperons the EOS becomes softer, and the maximum masses of neutron stars becomes smaller, compared with the case for npK- (K|—)0 matter. (K|—)0condensation makes the abundances of particles become identical leading to isospin saturated symmetric matter of antikaons, nucleons and hyperons. In the interior of massive neutron stars, neutron star matter including rich particle species, such as antikaons, nucleons and hyperons may exist. The deeper the optical potential of antikaons, the smaller the maximum masses of neutron stars. However a very deep optical potential of antikaon makes the baryon species appeared fewer.Also, with antikaon condensations we investigate the effect ofΔquartet in neutron star matter. According to the experimental data of the well-depth for hyperons and the masses of neutron stars from recent discoveries, we bound the range of K optical potentials and the relative coupling constants for hyperons, and obtain the set of hyperon coupling constants and the range of K optical potentials for neutron star matter including K condensations. The calculating results in the GL1 and NL-SH parameter sets show that K- and (K|—)0 condensations favor the appearances ofΔresonances. K- condensation makes the occurrences ofΔresonances earlier, whereas (K|—)0 condensation makes theΔquartet be close to isospin symmetry state. The appearances ofΔresonances change the composition and the distribution of particles at high densities. The populations ofΔresonances can enhance K- condensation, soften the EOS and further reduce the maximum masses of neutron stars.Finaly, The effects of antikaon condensations on the neutrino emitting and cooling of neutron stars are discussed. kURCA process corresponding to K- condensation is allowed in a wide density range, whereas k0URCA process corresponding to (K|—)0 condensation can only be allowed in a narrow density range at the core of neutron stars. The neutrino emissivity due to both K- and (K|—)0 condensations are large, with the order of 1025·erg·s-1·cm-3. Therefore, people commonly believe that antikaon condensations help fast cooling of neutron stars. However, the situation is complicated. With the model of weak interaction, where dURCA, kURCA and k0URCA processes can occur synchronously, we find that the three URCA processes influence each other. The neutrino emissivity due to dURCA process plays a dominating role, but antikaon condensations change the density range where dURCA process is allowed. In this case, the neutrino emissivity becomes lower. Though the neutrino emissivities for both of the kURCA and k0URCA processes contribute to the total neutrino emissivity, moreover the appearance of k0URCA process enhances the neutrino emissivity for kURCA, the total neutrino emissivity decreases all the same. It is found from the cooling curves of neutron stars that compared with np matter, antikaon condensations can hardly improve the cooling rate. It is also noted that the total neutrino luminosity increases with the neutron star mass, then it begins to fall over the maximum value in both np and npK- (K|—)0 matter. This means that the star with the mass larger than the maximal neutrino luminosity star may have a very slow cooling history, and we argue that the star can not exist stably from the view of the thermodynamics.
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