Kaon condensation in proto-neutron star matter

We study the equation of state of kaon-condensed matter including the effects of temperature and trapped neutrinos. Several different field-theoretical models for the nucleon-nucleon and kaon-nucleon interactions are considered. It is found that the order of the phase transition to a kaon-condensed phase, and whether or not Gibbs' rules for phase equilibrium can be satisfied in the case of a first order transition, depend sensitively on the choice of the kaon-nucleon interaction. To avoid the anomalous high-density behavior of previous models for the kaon-nucleon interaction, a new functional form is developed. For all interactions considered, a first order phase transition is possible only for magnitudes of the kaon-nucleus optical potential greater than or similar to 100 MeV. The main effect of finite temperature, for any value of the lepton fraction, is to mute the effects of a first older transition, so that the thermodynamics becomes similar to that of a second order transition. Above a critical temperature, found to be at least 30-60 MeV depending upon the interaction, the first order transition disappears. The phase boundaries in baryon density versus lepton number and baryon density versus temperature planes are delineated, which is useful in understanding the outcomes of proto-neutron star simulations. We find that the thermal effects on the maximum gravitational mass of neutron stars are as important as the effects of trapped neutrinos, in contrast to previously studied cases in which the matter contained only nucleons or in which hyperons and/or quark matter were considered. Kaon-condensed equations of State permit the existence of metastable neutron stars, because the maximum mass of an initially hot, lepton-rich proto-neutron star is greater than that of a cold, deleptonized neutron star. The large thermal effects imply that a metastable proto-neutron star's collapse to a black hole could occur much later than in previously studied cases that allow metastable configurations.