  The perturbation equation in a Kerr background is written as a coupled system
of one dimensional equations for the different modes in the time domain.
Numerical simulations show that the dominant mode in the gravitational response
is the one corresponding to the mode of the initial perturbation, allowing us
to conjecture that the coupling among the modes has a weak influence in our
system of equations. We conclude that by neglecting the coupling terms it can
be obtained a one dimensional harmonic equation which indeed describes with
good accuracy the gravitational response from the Kerr black hole with low
spin, while only few couplings are necessary to describe a high spin one. This
result may help to understand the structure of test fields in a Kerr background
and even to generate accurate waveforms for various cases in an efficient
manner.
