The relativistic Feynman-Metropolis-Teller theory for white-dwarfs in general relativity

TL;DR

This paper develops a relativistic model for white dwarf stars incorporating detailed atomic interactions and general relativity, refining previous models and affecting mass and radius predictions.

Contribution

It introduces a unified, self-consistent relativistic approach to white dwarf modeling that includes Coulomb interactions, eta-equilibrium, and quantum effects, extending classical theories.

Findings

Modified Chandrasekhar mass limit due to Coulomb and relativistic effects

Altered mass-radius relations for various white dwarf compositions

Quantitative impact of interactions on white dwarf stability

Abstract

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 \beta-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 $\sqrt{g_{00}}\mu_{\rm ws}$= constant, which links the chemical potential of the Wigner-Seitz cell $\mu_{\rm ws}$ 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 \beta-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.