Abstract

Black holes with hair represented by generic fields surrounding the central source of the vacuumSchwarzschild metric are examined under the minimal set of requirements consisting of (i) the exis-tence of a well defined event horizon, namely, we require the Killing horizon coincides with the causalhorizon and (ii) the strong or dominant energy condition for the hair outside the horizon. We developour analysis by means of the gravitational decoupling approach. We find that trivial deformationsof the seed Schwarzschild vacuum preserve the energy conditions and provide a new mechanismto evade the no-hair theorem based on a primary hair associated with the charge generating thesetransformations. Under the above conditions (i) and (ii), this charge consistently increases the entropyfrom the minimum value given by the Schwarzschild geometry. As a direct application, we find anon-trivial extension of the Reissner–Nordström black hole showing a surprisingly simple horizon.Finally, the non-linear electrodynamics generating this new solution is fully specified