Researchers have developed an analytical relativistic model for neutron stars that incorporates a mixed core of ordinary matter and dark matter. In this model, both types of matter coexist as independent, incompressible perfect fluids, interacting solely through the spacetime geometry. Ordinary matter extends throughout the star, while dark matter is confined exclusively to the core, forming an envelope of pure ordinary matter around this mixed core.

The main novelty of this work is the ability to keep the system analytically tractable, despite the complexity of a two-fluid core structure and an internal interface. This has allowed for explicit expressions for pressures and metric functions, facilitating the direct study of how the dark matter fraction and relative core size affect the star's properties. The model also determined the physically admissible parameter space and derived a Buchdahl-like critical compactness, linked to the divergence of central pressure, whose value depends on the relative dark matter density and the size of the mixed core.

The mass-radius analysis reveals that configurations with the same global compactness can exhibit very different internal matter distributions. In the one-fluid limit, the model recovers the Schwarzschild constant-density star and its standard critical value of 2M/R = 8/9. This construction not only provides an analytically controlled description of a core-confined second component but also serves as a valuable benchmark for identifying qualitative trends that can be explored in more realistic dark matter admixed neutron star models, whose detailed treatment is beyond the scope of this work.