  While no-hair theorems forbid isolated black holes from possessing permanent
moments beyond their mass, electric charge, and angular momentum, research over
the past two decades has demonstrated that a black hole interacting with a
time-dependent background scalar field will gain an induced scalar charge. In
this paper, we study this phenomenon from an effective field theory (EFT)
perspective. We employ a novel approach to constructing the effective
point-particle action for the black hole by integrating out a set of composite
operators localized on its worldline. This procedure, carried out using the
in-in formalism, enables a systematic accounting of both conservative and
dissipative effects associated with the black hole's horizon at the level of
the action. We show that the induced scalar charge is inextricably linked to
accretion of the background environment, as both effects stem from the same
parent term in the effective action. The charge, in turn, implies that a black
hole can radiate scalar waves and will also experience a "fifth force." Our EFT
correctly reproduces known results in the literature for massless scalars, but
now also generalizes to massive real scalar fields, allowing us to consider a
wider range of scenarios of astrophysical interest. As an example, we use our
EFT to study the early inspiral of a black hole binary embedded in a fuzzy dark
matter halo.
