Abstract
The mixed phase of quarks and hadrons which might exist in the dense matter encountered in the varying conditions of temperature and trapped neutrino fraction in proto-neutron stars is studied. We show that hadronic equations of state that maximize the quark content of matter at a given density generally minimize the extent of the mixed phase region in a neutron star of a given mass, and that only in extreme cases could a pure quark star result. Neutrino trapping inhibits the appearance of a mixed phase which leads to possible proto-neutron star metastability. We also demonstrate that the temperature along adiabats in the quark-hadron mixed phase is much smaller than what is found for the kaon condensate-hadron mixed phase. This could lead to core temperatures which are significantly lower in stars containing quarks than in those not containing quarks.
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