  A linear coupling between a scalar field and the Gauss-Bonnet invariant is
the only known interaction term between a scalar and the metric that: respects
shift symmetry; does not lead to higher order equations; inevitably introduces
black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus
on the simplest theory that includes such a term and we explore the dynamical
formation of scalar hair. In particular, we work in the decoupling limit that
neglects the backreaction of the scalar onto the metric and evolve the scalar
configuration numerically in the background of a Schwarzschild black hole or a
collapsing dust star described by the Oppenheimer-Snyder solution. For all
types of initial data that we consider, the scalar relaxes at late times to the
known, static, analytic configuration that is associated with a hairy,
spherically symmetric black hole. This suggests that the corresponding black
hole solutions are indeed endpoints of collapse.
