We study the properties of neutron star matter and neutron stars in th
e relativistic Brueckner-Hartree-Fock (RBHF) theory. Adopting the equa
tion of state (EOS) in the RBHF theory, we calculate the properties of
neutron star matter under the beta equilibrium condition in a wide ra
nge of density. We perform the Thomas-Fermi calculation of neutron sta
r matter in the crust region taking into account the change of nuclear
shapes around the density, rho similar to 10(14) g/cm(3). We compare
the results with the properties of dense matter in the non-relativisti
c many body theory. The qualitative feature of neutron star matter in
the crust is consistent with previous works. The relativistic EOS of n
eutron star matter is found to be stiffer than the non-relativistic EO
Ss characteristically. We found that the proton fraction of neutron st
ar matter in the high density region in the RBHF theory is quite large
as compared with those found in the non-relativistic calculations and
allow the direct Urea process, which is crucial for the rapid cooling
of neutron stars, for relatively massive neutron stars.