Neutron star equilibrium configurations within a fully relativistic theory with strong, weak, electromagnetic, and gravitational interactions

We formulate the equations of equilibrium of neutron stars taking into account strong, weak, electromagnetic, and gravitational interactions within the framework of general relativity. The nuclear interactions are described by the exchange of the sigma, omega, and rho virtual mesons. The equilibrium conditions are given by our recently developed theoretical framework based on the Einstein-Maxwell-Thomas-Fermi equations along with the constancy of the general relativistic Fermi energies of particles, the "Klein potentials", throughout the configuration. The equations are solved numerically in the case of zero temperatures and for selected parametrization of the nuclear models. The solutions lead to a new structure of the star: a positively charged core at supranuclear densities surrounded by an electronic distribution of thickness $\sim \hbar/(m_e c)$ of opposite charge, as well as a neutral crust at lower densities. Inside the core there is a Coulomb potential well of depth $\sim m_πc^2/e$. The constancy of the Klein potentials in the transition from the core to the crust, impose the presence of an overcritical electric field $\sim (m_π/m_e)^2 E_c$, the critical field being $E_c=m^2_e c^3/(e \hbar)$. The electron chemical potential and the density decrease, in the boundary interface, until values $μ^{\rm crust}_e < μ^{\rm core}_e$ and $ρ_{\rm crust}<ρ_{\rm core}$. For each central density, an entire family of core-crust interface boundaries and, correspondingly, an entire family of crusts with different mass and thickness, exist. The configuration with $ρ_{\rm crust}=ρ_{\rm drip}\sim 4.3\times 10^{11}$ g/cm$^3$ separates neutron stars with and without inner crust. We present here the novel neutron star mass-radius for the case $ρ_{\rm crust}=ρ_{\rm drip}$ and compare and contrast it with the one obtained from the Tolman-Oppenheimer-Volkoff treatment.

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