  Even though black hole scalarization is extensively studied recently, little
has been done in the direction of understanding the dynamics of this process,
especially in the rapidly rotating regime. In the present paper, we focus
exactly on this problem by considering the nonlinear dynamics of the scalar
field while neglecting the backreaction on the spacetime metric. This approach
has proven to give good results in various scenarios and we have explicitly
demonstrated its accuracy for nonrotating black holes especially close to the
bifurcation point. We have followed the evolution of a black hole from a small
initial perturbation, throughout the exponential growth of the scalar field
followed by a subsequent saturation to an equilibrium configuration. As
expected, even though the emitted signal and the time required to scalarize the
black hole are dependent on the initial perturbation, the final stationary
state that is reached is independent on the initial data.
