Hot super-dense compact object with particular EoS

We show the possibility of existence of a self-gravitating spherically-symmetric equilibrium configuration for a neutral matter with neutron-like density, small mass $M\ll M_{\odot }$, and small radius $R\ll R_{\odot }$. We incorporate the effects of both the special and general theories of relativity. Such object may be formed in a cosmic cataclysm, perhaps an exotic one. Since the base equations of hydrostatic equilibrium are completed by the equation of state (EoS) for the matter of the object, we offer a novel, interpolating experimental data from high-energy physics, EoS which permits the existence of such compact system of finite radius. This EoS model possesses a critical state characterized by density ${\rho }_c$ and temperature $T_c$. For such an object, we derive a radial distribution for the super-dense matter in "liquid" phase using Tolman–Oppenheimer–Volkoff equations for hydrostatic equilibrium. We demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. We derive the mass-radius relation (adjusted for relativistic corrections) for such small ($M\ll M_{\odot }$) super-dense compact objects. The results are within the constraints established by both heavy-ion collision experiments and theoretical studies of neutron-rich matter.