  We investigate the effects of dark matter (DM) on the nuclear equation of
state (EoS) and neutron star structure, in the relativistic mean field theory,
both in the absence and presence of a crust. The $\sigma$-$\omega$ model is
modified by adding a WIMP-DM component, which interacts with nucleonic matter
through the Higgs portal. This model agrees well with previous studies which
utilized either a more complicated nuclear model or higher-order terms of the
Higgs potential, in that DM softens the EoS, resulting in stars with lower
maximum masses. However, instabilities corresponding to negative pressure
values in the low-energy density regime of the DM-admixed EoS are present, and
this effect becomes more prominent as we increase the DM Fermi momentum. We
resolve this by confining DM in the star's core. The regions of instability
were replaced by three types of crust: first by an ideal gas EoS, then by the
Friedman-Pandharipande-Skyrme EoS, and finally the Skyrme Lyon EoS. While the
DM-admixed neutron star increases only slightly in its maximum mass with the
addition of the crust, the entire mass-radius relation of the neutron star is
significantly affected, with an observed increase in the radius of the star
corresponding to the mass.
