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In the context of the Minimal Geometric Deformation method, in this paper weimplement the inverse problem in a black hole scenario. In order to deal withan anisotropic polytropic black hole solution of the Einstein field equationswith cosmological constant, the deformation method is slightly extended. Afterobtaining the isotropic sector and the decoupler for an anisotropic (A-)dSpolytropic black hole solution, we emphasize a possible relation betweenanisotropization/isotropization and the violation of the energy conditions.

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