Abstract
We propose a relativistic model of compact star admitting conformal symmetry. Quark matter and baryonic matter which are considered as two different fluids, constitute the star. We define interaction equations between the normal baryonic matter and the quark matter and study the physical situations for repulsive, attractive and zero interaction between the constituent matters. The measured value of the Bag constant is used to explore the spacetime geometry inside the star. From the observed values of the masses of some compact objects, we have obtained theoretical values of the radii. Theoretical values of the radii match well with the previous predictions for such compact objects.
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