  We study the effects of dark matter on the structural properties of neutron
stars. In particular we investigate how the presence of a dark matter component
influences the mass-radius relation, the value of the maximum mass of a neutron
star and others stellar properties. To model ordinary matter we use a
state-of-the-art equation of state of $\beta$-stable nuclear matter obtained
using the Brueckner-Hartree-Fock quantum many-body approach starting from
two-body and three-body nuclear interactions derived from chiral effective
field theory. The dark matter component of the star is modeled as a
non-self-annihilating system of spin $1/2$ fermions and its equation of state
as an ideal relativistic Fermi gas. The equilibrium configurations of these
dark matter admixed neutron stars (DANS) are calculated by solving a
generalization of the Tolman-Oppenheimer-Volkoff equations to the case where
the system consists of two perfect fluids interacting solely through gravity.
We find that, depending on the dark matter particle mass $m_\chi$, one can have
somehow opposite effects on the stellar properties. In the case $m_\chi = 1\,
\mathrm{GeV}$, the stellar gravitational maximum mass $M_{max}$ decreases,
whereas in the case $m_\chi = 0.1\, \mathrm{GeV}$, $M_{max}$ increases with
respect to the maximum mass of ordinary neutron stars. We also show that the
presence of dark matter has indirect sizeable effect on the proton fraction in
the ordinary matter fluid and, in the case $m_\chi = 1\, \mathrm{GeV}$, results
in a decrease of the threshold gravitational mass $M_{tot}^{durca}$ for having
direct URCA processes and fast stellar cooling. Finally we study the stability
of dark matter admixed neutron stars with respect to radial perturbations.
