Neutron stars, with their extreme densities and intense gravitational fields, provide a natural laboratory for probing fundamental physics beyond the Standard Model—including potential signatures of dark matter. In this talk, I will present a fully relativistic analysis of radial oscillations and dynamical stability in neutron stars modeled as two-fluid systems, where nuclear matter and dark matter are treated as dynamically independent components coupled only through gravity. 

By solving the coupled relativistic perturbation equations and tracking the eigenfrequencies of the fundamental radial mode, I map out the stability boundaries of such stars across a two-dimensional space of central densities. A key result is the emergence of non-trivial stability surfaces, together with a generalized turning-point condition that accurately captures the onset of instability in these multi-fluid stars. I will also discuss how this two-fluid framework reveals new classes of stable neutron star configurations featuring ultra-dense interiors and twin-star structures — a phenomenon arising from the interplay between nuclear and dark matter microphysics.

If time permits, I will briefly discuss a complementary investigation in which the same two-fluid framework is used to constrain the microphysical properties of dark matter using astrophysical and cosmological observations. By confronting the theoretical predictions with gravitational-wave data (e.g., GW170817), NICER radius measurements, and constraints from galaxy cluster dynamics, we place stringent bounds on the mass and self-interaction strength of vector-mediated fermionic dark matter. This illustrates how multi-messenger observations, when combined with compact-star modeling, provide a way to probe the dark sector.