Relativistic star with Bose–Einstein condensate core and polytropic envelope in Karmarkar regime

A new anisotropic star model with core-envelope division is generated. The star is assumed to have the core composed of Bose–Einstein Condensate matter and polytropic envelope. The interior space-time is considered to be static and spherically symmetric in relativistic framework. We specify one of the gravitational potentials \(e^{\lambda }\) and \(e^{\nu }\) and then apply the Karmarkar condition to generate our model. The model formulated is free from central singularities and is verified by various stability tests and energy conditions. The equilibrium of the present model is examined by analysing TOV-equation. Stellar masses and radii of compact fluid spheres consistent with observations including Vela X-1, PSRJ1903+327, Cen X-3 and Her X-1 have been generated by using this model. The profiles for the matter variables in the present model are well behaved. It is entrancing to note that a multi-layered star model with core admitting Bose–Einstein condensate equation of state in embedding setting is missing in the previous studies.