Anisotropic compact stars in Rastall gravity: Neutron star models via minimal gravitational decoupling and the Karmarkar condition

In this study, we present two new anisotropic compact star models within the framework of Rastall gravity by employing the minimal geometric deformation scheme in conjunction with the Karmarkar embedding condition. The field equations for a system composed of two gravitationally interacting matter sources are effectively decoupled via a minimal geometric deformation of the radial metric component. The isotropic sector, treated as the seed solution, is derived using the Karmarkar condition, while the anisotropic sector is resolved through two distinct constraints: a barotropic equation of state and a mimic-pressure condition. The resulting anisotropic configurations are then analyzed using observational data from the compact star Cen X-3 ([Formula: see text]) for two values of the Rastall parameter, [Formula: see text] and [Formula: see text]. The derived models exhibit regular behavior of all physical variables and comply with the energy conditions, ensuring their physical viability. Stability is confirmed through the causality and adiabatic index criteria. These findings highlight the efficacy of this approach in Rastall gravity as a powerful tool for generating physically admissible models of anisotropic compact stars.