Minimal geometric deformation in asymptotically (A-)dS space-times and the isotropic sector for a polytropic black hole

In the context of the minimal geometric deformation method, in this paper we implement the inverse problem in a black hole scenario. In order to deal with an anisotropic polytropic black hole solution of the Einstein field equations with cosmological constant, the deformation method is slightly extended. After obtaining the isotropic sector and the decoupler for an anisotropic (A-)dS polytropic black hole solution, we emphasize a possible relation between anisotropization/isotropization and the violation of the energy conditions.