  Gravitational perturbations in a Kerr black hole background can not be
decomposed into simple tensor harmonics in the time domain. Here, we make the
mode decomposition only in the azimuthal direction and discuss the resulting
(2+1)-dimensional Klein-Gordon differential equation for scalar perturbations
with a two dimensional Dirac's $\delta$-function as a source representing a
point particle orbiting a much larger black hole. To make this equation
amenable for numerical integrations we explicitly remove analytically the
singular behavior of the source and compute a global effective source for the
corresponding waveform.
