  Effective theory of fluctuations based on underlying symmetry plays very
important role in understanding the low energy phenomena. Using this powerful
technique we study the fluctuation dynamics keeping in mind the following
central question: does the effective theory of black hole provide any
information about the possible existence of hair? Assuming the symmetry of the
hair being that of the underlying black hole space-time, we start by writing
down the most general action for the background and the fluctuation in the
effective field theory framework. Considering the asymptotically flat and de
Sitter black hole background with a spherically symmetric hair we derived the
most general equation of motion for the fluctuation. For a particular choice of
theory parameters, quasinormal modes corresponding to those fluctuations
appeared to have distinct features compared to that of the usual black hole
quasinormal modes. The background equations from the effective theory
Lagrangian, on the other hand, seemed to suggest that the underlying theory of
the hair under consideration should be higher derivative in nature. Therefore
as a concrete example we construct a class of higher derivative scalar field
theory which gives rise to spherically symmetric hair through background
cosmological constant. We also calculate the quasinormal modes whose behaviour
turned out to be similar to the one discussed from the effective theory.
