  We study the superradiant scattering of gravitational waves by a nearly
extremal black hole (dimensionless spin $a=0.99$) by numerically solving the
full Einstein field equations, thus including backreaction effects. This allows
us to study the dynamics of the black hole as it loses energy and angular
momentum during the scattering process. To explore the nonlinear phase of the
interaction, we consider gravitational wave packets with initial energies up to
$10%$ of the mass of the black hole. We find that as the incident wave energy
increases, the amplification of the scattered waves, as well as the energy
extraction efficiency from the black hole, is reduced. During the interaction
the apparent horizon geometry undergoes sizable nonaxisymmetric oscillations.
The largest amplitude excitations occur when the peak frequency of the incident
wave packet is above where superradiance occurs, but close to the dominant
quasinormal mode frequency of the black hole.
