Beyond classical anisotropy and a new look to relativistic stars: a gravitational decoupling approach

In this article, we propose a physical condition to extend interior isotropic solutions to anisotropic domains by gravitational decoupling in the framework of the Minimal Geometric Deformation approach. In particular, it is found that by using an expression reminiscent of the classical anisotropy factor, we can close the decoupling system of equations and a new anisotropic solution can be found. As an example, we extend the well--known Tolman IV.