  In this paper, we study the dynamics of scalar hair around a Schwarzchild
black hole. The scalar hair is sourced by the Gauss-Bonnet invariant with a
linear coupling. We work perturbatively in the coupling constant and ignore the
back-reaction of the scalar hair and the Gauss-Bonnet invariant. We evolve the
scalar field in the background of a Schwarzchild black hole and study the
dynamical formation of scalar hair with different self-interactions. We
integrate the energy and compute the energy flux of the scalar hair in terms of
the canonical energy-momentum tensor and give the corresponding dependence on
the self-interactions. Our results allow us to estimate the radiation and the
condensation of scalar field with different self-interactions, these would
improve our understanding for the dynamical scalarization of black holes and
the possible configuration of the scalar hair in scalar Gauss-Bonnet gravity.
