Asteroseismology and Universal Relations in Neutron Stars with Gravitationally Bound Dark Matter

We investigate the structural, dynamical, and oscillatory properties of neutron stars admixed with dark matter, modeled via a single-fluid formalism where dark matter interacts with nuclear matter through an effective Higgs-portal coupling. Employing three relativistic mean-field nuclear matter equations of state-IOPB-I, BigApple, and NL3- we incorporate a physically motivated dark matter number density profile that scales with baryon density and is controlled by two parameters: a scaling factor $\alpha M_\chi$ ($M_{\chi}$ being the mass of dark matter particle) and a steepness index $\beta$. We construct equilibrium configurations and analyze their stability via radial oscillations, finding that dark matter-induced gravitational compression lowers the maximum mass and alters the radial mode spectrum in a nontrivial, $\beta$-dependent fashion. We also compute the frequencies of non-radial fluid oscillations under the relativistic Cowling approximation and analyze the persistence of universal relations in the presence of dark matter. While deviations appear under extreme configurations, the overall structure of these relations remains robust. Our findings offer a consistent framework to probe dark matter effects on neutron star dynamics across a range of realistic models.