具有强、弱、电磁和引力相互作用的完全相对论理论中的中子星平衡构形
Neutron star equilibrium configurations within a fully relativistic theory with strong, weak, electromagnetic, and gravitational interactions
摘要：
在广义相对论的框架内，我们考虑了强、弱、电磁和引力相互作用，建立了中子星的平衡方程。核相互作用通过西格玛、欧米茄和ρ虚介子的交换来描述。平衡条件由我们最近发展的理论框架给出，该框架基于爱因斯坦-麦克斯韦-爱因斯坦-费米方程以及粒子的广义相对论费米能量的恒定性，“克莱因势”，在整个配置中。在零温度的情况下，并为选定的参数化的核模型的方程数值求解。解决方案导致一个新的结构的恒星：一个带正电的核心在超核密度包围的电子分布厚度$\sim \hbar/(m_e c)$相反的电荷，以及中性地壳在较低的密度。在核的内部有一个深度为$\sim m_πc^2/e$的库仑势阱。在从地核到地壳的过渡过程中，克莱因势的恒定性导致了超临界电场$\sim (m_π/m_e)^2 E_c$的存在，临界场为$E_c=m^2_e c^3/(e \hbar)$。在边界界面中，电子化学势和密度减小，直到值为$μ^{\rm crust}_e < μ^{\rm core}_e$和$ρ_{\rm crust}<ρ_{\rm core}$。对于每一个中心密度，都存在着一整套核壳界面边界，相应地，也存在着一整套质量和厚度不同的壳。具有$ρ_{\rm crust}=ρ_{\rm drip}\sim 4.3\times 10^{11}$ g/cm $^3$的配置将有和没有内壳的中子星分开。本文给出了$ρ_{\rm crust}=ρ_{\rm drip}$事例的中子星质量半径，并将其与Tolman-Oppenheimer-Escheroff处理得到的中子星质量半径进行了比较。
英文摘要：
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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