  We investigate how a spherically symmetric scalar field can modify the
Schwarzschild vacuum solution when there is no exchange of energy-momentum
between the scalar field and the central source of the Schwarzschild metric.
This system is described by means of the gravitational decoupling by Minimal
Geometric Deformation (MGD-decoupling), which allows us to show that, under the
MGD paradigm, the Schwarzschild solution is modified in such a way that a naked
singularity appears.
