• black hole hair
• black holes
• effective field theory
• General Relativity
• massive vector field
• no-hair conjecture
• no-hair theorems
• scalar-tensor theories
• shift symmetric scalar field
• vector-tensor theories

With the recent successes and the future prospects in gravitational interferometry, the study of black hole hair gains today a strong phenomenological motivation.
Investigating the presence of hair within the framework of effective field theory is particularly convenient in order to capture the relevant low energy features of generic models describing gravity coupled to additional fields.

The present work follows this line of research, focusing on shift symmetric scalar-tensor models and vector-tensor models.

In the scalar context, I review a recent, rather general no-hair theorem and I analyse its possible violations, till date only partially understood. In doing so I present an original way to evade the theorem, that is having non-vanishing hair at infinity in an asymptotically flat space-time.
Throughout the work I examine whether or not the various hairy solutions violating the theorem are acceptable from the effective field theory point of view.

Moreover, motivated by a connection between shift symmetric scalar-tensor and vector-tensor models, I study to which extent the scalar no-hair theorem can be translated to the vector case.

The same connection makes possible to analyse the newly-found class of scalar hairy solutions and its vector counterpart at the same time.
Studying this class provides new information about the violations of the scalar no-hair theorem and helps to rethink certain common beliefs regarding vector hair.