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 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 $\mathrm{\Lambda }$ ($f_{\max }-{\mathrm{\Lambda }}_{1.4}$).

The properties of a neutron star are studied in the presence of dark matter. We have considered a relatively light weakly interacting massive particle (WIMP) as a dark matter candidate with properties suggested by the results of the DAMA/LIBRA collaboration, realized for instance within the framework of the Next-to-Minimal Supersymmetric Standard Model. The dark matter particle interacts with the baryonic matter of a neutron star through Higgs bosons. The dark matter variables are essentially fixed using the results of the DAMA/LIBRA experiment, which are then used to build the Lagrangian density for the WIMP–nucleon interaction inside a neutron star. We have used the effective field theory motivated relativistic mean field model to study the equations-of-state in the presence of dark matter. The predicted equations-of-state are used in the Tolman–Oppenheimer–Volkoff equations to obtain the mass–radius relations, the moment of inertia, and effects of the tidal field on a neutron star. The calculated properties are compared with the corresponding data of the GW170817 event.

The neutron star properties are generally determined by the equation of state of $\beta$-equilibrated dense matter. In this work, we consider the interaction of fermionic dark matter (DM) particles with nucleons via Higgs exchange and investigate the effect on the neutron star properties with the relativistic mean-field model equation of state coupled with DM. We deduce that DM significantly affects the neutron star properties, such as considerably reducing the maximum mass of the star, which depends on the percentage of the DM considered inside the neutron star. The tidal Love numbers both for electric and magnetic cases and surficial Love numbers are also studied for DM admixed NS. We observed that the magnitude of tidal and surficial Love numbers increases with a greater DM percentage. Further, we present post-Newtonian tidal corrections to gravitational waves decreased by increasing the DM percentage. The DM effect on the GW signal is significant during the late inspiral and merger stages of binary evolution for GW frequencies >500 Hz.

We study the thermal effects on the nuclear matter (NM) properties such as binding energy, incompressibility, free symmetry energy and its coefficients using NL3, G3 and IU-FSU parameter sets of relativistic mean-field models. These models being consistent with the properties of cold NM, have also been used to study the effect of temperature by incorporating the Fermi function. The critical temperature for the liquid-gas phase transition in the symmetric NM is found to be 14.60, 15.37 and 14.50 MeV for NL3, G3 and IU-FSU parameter sets respectively, which is in excellent agreement with previous theoretical and experimental studies. We inspect that the properties related to second differential coefficient of the binding energy and free symmetry energy at saturation density ( i.e. $$K_{0}(n,T)$$K0(n,T) and $$Q_{sym,0}$$Qsym,0 ) exhibit the contrary effects for NL3 and G3 parameters as the temperature increases. We find that the prediction of saturated curvature parameter ( $$K_{sym,0}$$Ksym,0 ) for G3 equation of state at finite temperature favour the combined analysis of $$K_{sym,0}$$Ksym,0 for the existence of massive pulsars, gravitational waves from GW170817 and NICER observations of PSR J0030+0451. Further, we investigate the cooling mechanism of newly born stars through neutrino emissivity controlled by direct Urca process and instate some interesting remarks about neutrino emissivity. We also deliberate the effect of temperature on the M-R profile of Proto-Neutron star.