  In this work we construct a static and spherically symmetric black hole
geometry supported by a family of generic mono-parametric sources thorough the
Gravitational Decoupling. The parameter characterizing the matter sector can be
interpreted as hair which cannot be associated to any global charge. Although
the solution is constructed by demanding the weak energy condition, we find
that the resulting matter sector satisfies all the energy conditions at and
outside the horizon. We study the effect of the hair on the periastron advance
and the gravitational lensing of the black hole. We estimate the best WKB order
to compute the quasinormal frequencies for scalar, vector and tensor
perturbation fields.

General Relativity and Quantum Cosmology