Implications of gravitational decoupling on energy exchange of extended Einstein’s universe solution

Abstract This study presents the development of a new, physically viable, compact stellar model using the theoretical framework of gravitational decoupling by extended minimal geometric deformation. This model is constructed using the well-known cosmological solution of the Einstein universe as an initial metric, and the effective system satisfies the Karmarkar condition. Furthermore, we analyse the dynamics of energy exchange between the constituent fluids of the effective compact object. Our findings show that the system is sustained by an energy exchange from an unknown source to the Einstein universe fluid, with this exchange being more pronounced when this cosmological fluid has higher energy density. This exchange is most intense in the outermost regions of the compact stellar body that supports both fluids.