  The properties of neutron stars are investigated within the relativistic
central variational method by using a realistic nucleon-nucleon ($NN$)
interaction. The strong repulsion of realistic $NN$ interactions at short
distances is treated by a Jastrow central correlation function, whose form is
completely determined through minimization of the total energy of the nuclear
many-body system. The relativistic Hartree-Fock wave functions are chosen as
the trial wave function. In this framework, the equation of state of the
neutron star matter in $\beta$ equilibrium is obtained self-consistently. We
further determine the properties of neutron stars via the
Tolman-Oppenheimer-Volkoff equation using Bonn A, B, and C potentials. The
maximum masses of neutron stars with these realistic potentials are around
$2.18 M_\odot$ and their corresponding radii are around $11$ km. These results
are in accordance with the calculations of the relativistic
Brueckner-Hartree-Fock theory with the same potentials. Furthermore, we also
find that the splitting of proton-neutron effective masses will be reversed at
high density in the neutron star matter, which are caused by the contribution
of short-range correlation on kinetic energy.
