  The scalarization is a very interesting phenomena allowing to endow a compact
object with scalar hair while leaving all the predictions in the weak field
limit unaltered. In Gauss-Bonnet gravity the source of the scalar field can be
the curvature of the space-time. It was recently shown that for a particular
type of coupling function between the scalar field and the Gauss-Bonnet
invariant, spin-induced black hole scalarization is possible. In the present
paper we study this phenomenon by performing a 2+1 time evolution of the
relevant linearized scalar field perturbation equation and examine the region
where the Kerr black hole becomes unstable giving rise to new scalarized
rotating black holes. This is more direct numerical approach to study the
development of spin-induced scalarization and it can serve as an independent
check of the previous results.
