  The relativistic neutrino emissivity of the nucleonic direct URCA processes
in neutron star matter are investigated within the relativistic Hartree-Fock
approximation. We study particularly the influences of the tensor couplings of
vector mesons $\omega$ and $\rho$ on the nucleonic direct URCA processes. It is
found that the inclusion of the tensor couplings of vector mesons $\omega$ and
$\rho$ can slightly increase the maximum mass of neutron stars. In addition,
the results indicate that the tensor couplings of vector mesons $\omega$ and
$\rho$ lead to obvious enhancement of the total neutrino emissivity for the
nucleonic direct URCA processes, which must accelerate the cooling rate of the
non-superfluid neutron star matter. However, when considering only the tensor
coupling of vector meson $\rho$, the neutrino emissivity for the nucleonic
direct URCA processes slightly declines at low densities and significantly
increases at high densities.That is to say that the tensor coupling of vector
meson $\rho$ leads to the slow cooling rate of a low-mass neutron star and
rapid cooling rate of a massive neutron star.
