Abstract
We present a singularity free and smoothly connected complete solution for a three-layered compact star with deconfined quark matter core surrounded by coherent quantum fluid of a Bose-Einstein condensate, all enclosed under a thin envelope of a repulsive neutron-Coulomb fluid. A modified form of Buchdahl-I type spatial metric is used as a seed to obtain the explicit temporal metric potential for each layer using Einstein field equation. The process allows us to obtain insights into the pressure-density profile and associated thermodynamic properties within stellar interior, shedding light on its structural stability, mass-radius relation and physical plausibility. One of the key finding of our work is the close similarity between the M–R curve of our three-phase model star VelaX-1 and that of a strange quark star model.
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