  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.
