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An alternative method of calculating the waveforms generated during a binary
inspiral is provided by black hole perturbation theory.
In the limit of a small mass ratio
test mass limit) we can treat the effects of the smaller body as perturbations of
the gravitational field of the larger mass. If the latter is a black hole then
the Teukolsky formalism  can be used to calculate these perturbations.
The corrections to
the metric are then expressed as an infinite sum over multipole
moments. Here we will consider the case of a Schwarzschild black hole.
GRASP Routines: Waveforms from perturbation theory