Kaon condensation in proto-neutron star matter - art. no. 035803

We study the equation of state of kaon-condensed matter including the effec ts of temperature and trapped neutrinos. Several different field-theoretica l models for the nucleon-nucleon and kaon-nucleon interactions are consider ed. 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 satisfi ed in the case of a first order transition, depend sensitively on the choic e of the kaon-nucleon interaction. To avoid the anomalous high-density beha vior of previous models for the kaon-nucleon interaction, a new functional form is developed. For all interactions considered, a first order phase tra nsition is possible only for magnitudes of the kaon-nucleus optical potenti al greater than or similar to 100 MeV. The main effect of finite temperatur e, 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 s econd order transition. Above a critical temperature, found to be at least 30-60 MeV depending upon the interaction, the first order transition disapp ears. The phase boundaries in baryon density versus lepton number and baryo n density versus temperature planes are delineated, which is useful in unde rstanding the outcomes of proto-neutron star simulations. We find that the thermal effects on the maximum gravitational mass of neutron stars are as i mportant as the effects of trapped neutrinos, in contrast to previously stu died cases in which the matter contained only nucleons or in which hyperons and/or quark matter were considered. Kaon-condensed equations of State per mit 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 met astable proto-neutron star's collapse to a black hole could occur much late r than in previously studied cases that allow metastable configurations.