An EGD model in the background of embedding class I space-time

This work is devoted to the study of relativistic anisotropic compact objects. To obtain this class of solutions of the Einstein field equations, we have developed a general scheme to generate the metric of the space-time describing the interior of the compact structure. This approach is based on the class I space-time and the extended gravitational decoupling by means of an extended geometric deformation (EGD). The class I condition provides a differential equation relating both metric potential nu and lambda, whilst the EGD translates the metric potentials to nu=xi+beta f(r)], where h(r) and f(r) are the deformation functions and beta a dimensionless constant. In this case the pair {xi,mu} represents the seed solution satisfying the class I condition without any deformation. Once the deformed metric potentials are inserted into the class I, the main task is to obtain h(r) or f(r). So, in this case a particular ansatz for h(r) is considered in conjunction with beta =0.5 to get f(r). In order to check feasibility of our model, we have performed a thoroughly physical, mathematical and graphical analysis.