Two-layered compact star in biquadratic spatial metric with distinct core-shell equations of state

We develop a smoothly matched and singularity-free model for a two-layered compact star, comprising an MIT bag model type dense core surrounded by a shell of Bose-Einstein condensate. Using a biquadratic spatial metric as the coherent background, the temporal metric potential for each layer is obtained by solving the Einstein field equations. This approach provides a comprehensive understanding of the pressure-density distribution and thermodynamic behavior within the star, offering critical insights into its stability, mass-radius relationship, and overall physical feasibility. A key finding of this study is the existence of a stable core-shell structure, where the two distinct regions are smoothly connected at the junction

. Another distinctive feature is the formation of a uniform flow zone close to core-shell junction, where the tangential sound speed remains nearly constant $v_{ts,c}\left(r\right)\approx 0.374$.