Gravitational Decoupling as a Generator of Curvature and Matter Distribution

In this work, we generate curved Lorentzian manifolds from a flat Minkowskian space–time, through the Gravitational Decoupling by the Minimal Geometric Deformation method interpreting the decoupling sector as a generator of curvature and matter distribution. In particular, we obtain some new wormhole geometries by imposing either physically relevant equations of state or certain physically–motivated geometric constraints. These solutions are analyzed in detail. For all these solutions, we study the associated energy conditions, the geometric behavior and construct their embedding diagrams.