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We parameterize the core of compact spherical star configurations by a mass($m_x$) and a radius ($r_x$) and study the resulting admissible areas in thetotal-mass vs. total-radius plane. The employed fiducial equation-of-statemodels of the corona at radii $r \ge r_x$ and pressures $p \le p_x = p(r =r_x)$ are that (i) of constant sound velocity and (ii) a proxy of DY$\Delta$DD-ME2 provided by Buchdahl's exactly solvable ansatz. The core ($r < r_x$) maycontain any type of material, e.g. Standard-Model matter with unspecifiedequation of state or/and an unspecified Dark-Matter admixture. Employing a toymodel for the cool equation of state with first-order phase transition wediscuss also the mass-radius relation of compact stars with an admixture ofDark Matter in a Mirror-World scenario.

Exotic Cores with and without Dark-Matter Admixtures in Compact Stars