Black holes with hair represented by generic fields surrounding the central
source of the vacuum Schwarzschild metric are examined under the minimal set of
requirements consisting of i) the existence of a well defined event horizon and
ii) the strong or dominant energy condition for the hair outside the horizon.
We develop our analysis by means of the gravitational decoupling approach. We
find that trivial deformations of the seed Schwarzschild vacuum preserve the
energy conditions and provide a new mechanism to evade the no-hair theorem
based on a primary hair associated with the charge generating these
transformations. Under the above conditions i) and ii), this charge
consistently increases the entropy from the minimum value given by the
Schwarzschild geometry. As a direct application, we find a non-trivial
extension of the Reissner-Nordstrom black hole showing a surprisingly simple
horizon. Finally, the non-linear electrodynamics generating this new solution
is fully specified.Comment: 11 pages, 4 figure
