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We investigate the effects of dark matter (DM) on the nuclear equation ofstate (EoS) and neutron star structure, in the relativistic mean field theory,both in the absence and presence of a crust. The $\sigma-\omega$ model ismodified by adding a WIMP-DM component, which interacts with nucleonic matterthrough the Higgs portal. This model agrees well with previous studies whichutilized either a more complicated nuclear model or higher-order terms of theHiggs potential, in that DM softens the EoS, resulting in stars with lowermaximum masses. However, instabilities corresponding to negative pressurevalues in the low-energy density regime of the DM-admixed EoS are present, andthis effect becomes more prominent as we increase the DM Fermi momentum. Weresolve this by confining DM in the star's core. The regions of instabilitywere replaced by three types of crust: first by theFriedman-Pandharipande-Skyrme (FPS), Skyrme-Lyon (SLy) and BSk19 EoS from theBrussels-Montreal Group, which can be represented by analytical approximations.For a fixed value of the DM Fermi momentum $p_F^{DM}$, the DM-admixed neutronstar does not have significant changes in its mass with the addition of thecrusts. However, the entire mass-radius relation of the neutron star issignificantly affected, with an observed increase in the radius of the starcorresponding to the mass. The effect of DM is to reduce the mass of the star,while the crust does not affect the radius significantly, as the value of the$p_F^{DM}$ increases.

Stability of Neutron Stars with Dark Matter Core Using Three Crustal Types and the Impact on Mass-Radius Relations