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The effect of temperature and density dependence of the asymmetric nuclearmatter properties is studied within the extended relativistic mean field (ERMF)model, which includes the contribution from the self and mixed interactionterms by using different parametrizations obtained by varying the neutron skinthickness $\Delta$r and $\omega$-meson self-coupling ($\zeta$). We observedthat the symmetry energy and its slope and incompressibility coefficientsdecrease with increasing temperatures up to saturation densities. The ERMFparametrizations were employed to obtain a new set of equations of state (EOS)of the protoneutron star (PNS) with and without inclusion of hyperons. In ourcalculations, in comparison with cold compact stars, we obtained that thegravitational mass of the protoneutron star with and without hyperons increasedby $\sim 0.4M_{\odot}$ and its radius increased by $\sim 3$km. Whereas in caseof the rotating PNS, the mass shedding limit decreased with increasingtemperature, and this suggested that the keplerian frequency of the PNS, at T =10 MeV should be smaller by $14-20%$ for the EOS with hyperon, as compared tothe keplerian frequency of a cold compact star.

Temperature and density dependence of asymmetric nuclear matter and protoneutron star properties within an extended relativistic mean field model