Numerical Modeling of Thermodynamic Parameters for Hot Neutron Star Matter in Neutrino-Trapped Regime

We investigate the thermodynamic properties of the hot $$\beta $$ -equilibrated hadronic matter which consists of neutrons, protons, electrons, electron neutrinos, muons, and muon neutrinos. To describe such matter, we use an improved version of the relativistic mean field (RMF) theory at a finite temperature, where, in addition to the effective fields of $$\sigma $$ -, $$\omega $$ -, and $$\rho $$ -mesons, the isovector, Lorentz-scalar $$\delta $$ -meson effective field is also taken into account. The numerical solution of systems of ten nonlinear algebraic equations allows us to obtain the meson mean-fields $$\bar {\sigma }$$ , $$\bar {\omega }$$ , $$\overline \delta $$ and $$\bar {\rho }$$ , as well as the chemical potentials of the particles $${{\mu }_{n}}$$ , $${{\mu }_{p}}$$ , $${{\mu }_{e}}$$ , $${{\mu }_{\mu }}$$ , $${{\mu }_{{{{\nu }_{e}}}}}$$ , and $${{\mu }_{{{{\nu }_{\mu }}}}}$$ . This made it possible, for given values of temperature $$T$$ and baryon number density $${{n}_{{\text{B}}}}$$ , to calculate the energy density $$\epsilon $$ , pressure $$P$$ , and entropy density $$S$$ of hadronic matter in the neutrino trapped regime.