广义相对论中白矮星的相对论Feynman-Metropolis-Teller理论
The relativistic Feynman-Metropolis-Teller theory for white-dwarfs in general relativity
摘要：
在压缩原子的Feynman-Metropolis-Teller理论中，最近提出的相对论性的B-Fermi模型被应用于广义相对论性白矮星平衡位形的研究.考虑了β平衡、原子核相互作用以及原子核与周围电子之间的库仑相互作用，并将每个原子约束在Wigner-Seitz盒中，得到了作为压缩函数的物态方程。量子统计、弱相互作用、核相互作用和电磁相互作用的贡献是通过确定Wigner-Seitz盒的化学势得到的。白矮星物质的广义相对论平衡的进一步贡献可以用简单的公式$\sqrt{g_{00}}μ_{\rm ws}$ =常数来表示，它将维格纳-塞茨盒$μ_{\rm ws}$的化学势与组态中每一点的广义相对论引力势$g_{00}$联系起来。每个维格纳-塞茨盒外的结构都是严格中性的，因此不需要全局电场来保证白矮星的平衡。这些方程通过适当考虑原子核和电子之间的库仑相互作用以及逆β衰变来修改了Erasekhar使用的方程。他们还概括了Salpeter的工作，通过考虑一个统一的自洽方法在每个Wigner-Seitz细胞的库仑相互作用。给出了对$^4$ He、$^{12}$ C、$^{16}$ O和$^{56}$ Fe白矮星的质量-半径关系以及对P-L质量极限的数值的影响。在需要精确了解白矮星参数的过程中，应考虑到所有这些影响。
英文摘要：
The recent formulation of the relativistic Thomas-Fermi model within the Feynman-Metropolis-Teller theory for compressed atoms is applied to the study of general relativistic white dwarf equilibrium configurations. The equation of state, which takes into account the β-equilibrium, the nuclear and the Coulomb interactions between the nuclei and the surrounding electrons, is obtained as a function of the compression by considering each atom constrained in a Wigner-Seitz cell. The contribution of quantum statistics, weak, nuclear, and electromagnetic interactions is obtained by the determination of the chemical potential of the Wigner-Seitz cell. The further contribution of the general relativistic equilibrium of white dwarf matter is expressed by the simple formula $\sqrt{g_{00}}μ_{\rm ws}$= constant, which links the chemical potential of the Wigner-Seitz cell $μ_{\rm ws}$ with the general relativistic gravitational potential $g_{00}$ at each point of the configuration. The configuration outside each Wigner-Seitz cell is strictly neutral and therefore no global electric field is necessary to warranty the equilibrium of the white dwarf. These equations modify the ones used by Chandrasekhar by taking into due account the Coulomb interaction between the nuclei and the electrons as well as inverse β-decay. They also generalize the work of Salpeter by considering a unified self-consistent approach to the Coulomb interaction in each Wigner-Seitz cell. The consequences on the numerical value of the Chandrasekhar-Landau mass limit as well as on the mass-radius relation of $^4$He, $^{12}$C, $^{16}$O and $^{56}$Fe white dwarfs are presented. All these effects should be taken into account in processes requiring a precision knowledge of the white dwarf parameters.
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