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Protoneutron stars are hot and lepton rich objects formed in type II supernovae. It is natural to regard the evolution of these stars as taking place in several stages. This paper describes results of analysis of protoneutron star evolution for models incorporating an strangeness-rich, neutrino opaque matter equation of state. Of special interest in this paper is the comparison of protoneutron star models for two different phases. One characterized by neutrino trapping and by the value of entropy s=1 and the other, formed when neutrinos leak out of the system, described as a hot deleptonized star. The equation of state adequate for the protoneutron star has been constructed. It has been shown that the maximum stable protoneutron star mass is close to 1.44 M_⊙.

The properties of massive protoneutron stars (PNSs) are of great significance for the study of supernova and the evolution of neutron stars or black holes. The mass of the massive neutron star PSR J1614-2230 is fitted by selecting the nuclear coupling constants and adjusting the hyperon coupling constants in the framework of the relativistic mean field (RMF) theory. The model is then extrapolated to calculate the properties of massive PNS with the trapped neutrinos. The effects of different trapped neutrinos on the composition and structure of massive PNSs are discussed for entropy per baryon $S=1$. Results show that the presence of trapped neutrinos increase the energy density. Moreover, the significant neutrinos trapped, such as electron leptons number $Y_L=0.4$, reduces the pressure of massive PNSs in the density region 0.2–0.5fm${}^{-3}$, that is to say, the equation-of-state (EOS) is softened in this region. The maximum masses and corresponding radii of massive PNSs are calculated to be 2.110$M_{\odot }$, 2.106$M_{\odot }$, 2.095$M_{\odot }$, 2.082$M_{\odot }$ and 12.19, 11.88, 11.75 and 11.81 km for the electron leptons number $Y_L=0.1,0.2,0.3,0.4$. We calculate the distribution of the internal temperature, and get the effects of the trapped neutrinos on the internal temperature of massive PNSs for the first time. For the different electron leptons number $Y_L=0.1,0.2,0.3,0.4$, the central temperatures of the massive PNS, when the mass is taken to be the same as that of the observed neutron star PSR J1614-2230$(1.97\pm 0.04M_{\odot })$, are $19.57_{-0.19}^{+0.32}$, $22.55_{-0.25}^{+0.36}$, $25.48_{-0.45}^{+0.68}$, $27.47_{-0.83}^{+0.93}$MeV, respectively.

Thermodynamical properties of nuclear matter are studied in the framework of an effective many-body field theory at finite temperature, considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Trapped neutrinos are also included in order to describe protoneutron star properties through the integration of the Tolman–Oppenheimer–Volkoff equations, from which we obtain, beyond the standard relations for the masses and radii of protoneutron stars as functions of the central density, new results of these quantities as functions of temperature. Our predictions include: the determination of an absolute value for the limiting mass of protoneutron stars; new structural aspects on the nuclear matter phase transition via the behavior of the specific heat and, through the inclusion of quark degrees of freedom, the properties of a hadron-quark phase transition and hybrid protoneutron stars