We study the dark matter (DM) effects on the nuclear matter (NM) parameters characterizing the equation of states of super dense neutron-rich nucleonic matter. The observables of the NM, i.e. incompressibility, symmetry energy and its higher order derivatives in the presence DM for symmetric and asymmetric NM are analysed with the help of an extended relativistic mean field model. The calculations are also extended to β-stable matter to explore the properties of the neutron star (NS). We analyse the DM effects on symmetric NM, pure neutron matter, and NS using NL3, G3, and IOPB-I forces. The binding energy per particle and pressure is calculated with and without considering the DM interaction with the NM systems. The influences of DM are also analysed on the symmetry energy and its different coefficients. The incompressibility and the skewness parameters are affected considerably due to the presence of DM in the NM medium. We extend the calculations to the NS and find its mass, radius and the moment of inertia for static and rotating NS with and without DM contribution. The mass of the rotating NS is considerably changing due to rapid rotation with the frequency in the mass-shedding limit. The effects of DM are found to be important for some of the NM parameters, which are crucial for the properties of astrophysical objects.

We put constraints on the secondary component of GW190814 by analyzing the observational data of the event. The relativistic mean-field models are used to calculate the mass-radius profile and tidal deformability of the compact object, considering it as a massive neutron star with the presence of dark matter particles inside it. With the increase of dark matter percentage, the maximum mass, radius, and tidal deformability of the neutron star decreases. We observe that the predicted properties are well consistent with GW190814 observational data, suggesting the possibility of a dark matter admixed neutron star if the underlying nuclear equation of state is sufficiently stiff.

We investigate the $f$-mode oscillation of the dark matter admixed hyperon star within the relativistic Cowling approximation. The macroscopic properties are calculated with the relativistic mean-field equation of states by assuming that the dark matter particles are inside the star. The $f$-mode oscillation frequencies (only for $l=2$) are calculated with four different neutron star equation of states. We also check the effects of hyperons/dark matter and hyperons with dark matter equation of states on the $f$-mode oscillations varying with different astrophysical quantities such as mass ($M$), radius ($R$), compactness ($M/R$), surface red-shift ($Z_s$), average density ($\overline{\rho }$), and dimensionless tidal deformability ($\mathrm{\Lambda }$) of the neutron star. Significant changes have been seen in the $f$-mode frequencies with and without hyperons/dark matter or $\mathrm{hyperons}+\mathrm{dark}$ matter. Substantial correlations are observed between canonical frequencies and $\mathrm{\Lambda }$ ($f_{1.4}-{\mathrm{\Lambda }}_{1.4}$) and maximum frequencies and canonical $\mathrm{\Lambda }$ ($f_{\max }-{\mathrm{\Lambda }}_{1.4}$).

Using the relativistic mean-field model, we calculate the properties of binary neutron star (BNS) in the in-spiral phase. Assuming the dark matter (DM) particles are accreted inside the neutron star (NS) due to its enormous gravitational field, the mass M, radius R, tidal deformability λ and dimensionless tidal deformability Λ are calculated at different DM fractions. The value of M, R, λ and Λ decreases with the increase of DM percentage inside the NS. The in-spiral phase properties of the BNS are explored within the post-Newtonian (PN) formalism, as it is suitable up to the last orbits in the in-spiral phase. We calculate the strain amplitude of the polarization waveform h₊ and h_×, (2,2) mode waveform h₂₂, orbital phase Φ, frequency of the gravitational wave f and PN parameter x with DM as an extra candidate inside the NS. The magnitude of f, Φ and x are almost the same for all assumed forces; however, the in-spiral time duration in the last orbit is different. We find that the BNS with soft equation of state and a high fraction of DM sustains more time in their in-spiral phase. We suggest that one should take DM inside the NS when they modelling the in-spiral waveforms for the BNS systems.

Within the relativistic mean-field model, we investigate the properties of dark matter (DM) admixed neutron stars, considering nonrotating objects made of isotropic matter. We adopt the IOPB-I hadronic equation of state (EOS) by assuming that the fermionic DM within supersymmetric models has already been accreted inside the neutron star (NS). The impact of DM on the mass-radius relationships and the radial oscillations of pulsating DM admixed neutron stars (with and without the crust) are explored. It is observed that the presence of DM softens the EOS, which in turn lowers the maximum mass and its corresponding radius. Moreover, adding DM results in higher frequencies of pulsating objects, and hence we show the linearity of the fundamental mode frequency of canonical NS with DM Fermi momentum. We also investigate the profile of eigenfunctions solving the Sturm-Liouville boundary value problem and verify its validity. Further, we study the stability of NSs considering the fundamental mode frequency variation with the mass of the star and verify the stability criterion $\partial M/\partial {\rho }_c>0$. Finally, the effect of the crust on the large frequency separation for different DM Fermi momenta is shown as well.