  This thesis explores the effects of dark matter (DM) on neutron stars (NSs)
using the relativistic mean-field (RMF) model. The effects of DM on NS
properties, including the mass-radius relation, the moment of inertia, and
tidal deformability, are calculated by varying its fraction. The study found
that the EOS becomes softer with increasing DM momentum, and the DM has
marginal effects on nuclear matter properties, except for the EOSs and binding
energy per particle. The study also calculated the properties of isolated,
static, and rotating DM admixed NS and found that the DM has significant
effects on both static and rotating NS. We have also observed that a tiny
amount of DM can accumulate inside the NS, and more amount of it makes the NS
unstable. The study also suggests that the secondary component might be a NS
with DM content if the underlying nuclear EOS is sufficiently stiff. The
$f$-mode oscillations of the DM admixed hyperon stars are calculated and found
that there exist a correlation between canonical $f$-mode frequency and the
dimensionless tidal deformability parameter ($\Lambda_{1.4}$) and we have put a
constraint on $f$-mode frequency using GW170817 data. Finally, we have
calculated the DM admixed binary NS properties and found that the binary system
becomes less deformed and sustains more time in its inspiral phases with the
addition of DM. Therefore, we suggest that one can take DM inside the compact
objects while modeling the inspiral waveforms for the BNS systems.
