Spherical configuration of a super-dense hot compact object with particular EoS

The equation of state (EoS) $P=P(\rho ,\mathrm{.}\mathrm{.}\mathrm{.})$ – pressure as a function of density and other thermodynamical quantities – is what generates particularities of mass–radius distribution $M(R)$ for super–dense compact stellar bodies, the remnants of cosmic cataclysms. In view of recent nuclear experiments, we propose one particular EoS, which admits the critical state characterized by density ${\rho }_c$ and temperature $T_c$, and which under certain conditions permits a radial distribution of the super–dense matter in “liquid” phase. We establish such conditions and demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. Using Tolman–Oppenheimer–Volkoff equations for hydrostatic equilibrium, we derive the mass–radius relation for the super–dense compact objects with masses smaller than the Sun, $M\ll M_{\odot }$. The obtained results are within the constraints established by both heavy–ion collision experiments and theoretical studies of neutron–rich matter.