  We adapt a method of matching post-Newtonian and black-hole-perturbation
theories on a timelike surface (which proved useful for understanding head-on
black-hole-binary collisions) to treat equal-mass, inspiralling black-hole
binaries. We first introduce a radiation-reaction potential into this method,
and we show that it leads to a self-consistent set of equations that describe
the simultaneous evolution of the waveform and of the timelike matching
surface. This allows us to produce a full inspiral-merger-ringdown waveform of
the l=2, m=2,-2 modes of the gravitational waveform of an equal-mass
black-hole-binary inspiral. These modes match those of numerical-relativity
simulations well in phase, though less well in amplitude for the inspiral. As a
second application of this method, we study a merger of black holes with spins
antialigned in the orbital plane (the "superkick" configuration). During the
ringdown of the superkick, the phases of the mass- and current-quadrupole
radiation become locked together, because they evolve at the same quasinormal
mode frequencies. We argue that this locking begins during merger, and we show
that if the spins of the black holes evolve via geodetic precession in the
perturbed black-hole spacetime of our model, then the spins precess at the
orbital frequency during merger. In turn, this gives rise to the correct
behavior of the radiation, and produces a kick similar to that observed in
numerical simulations.
