  We derive the Teukolsky equation for perturbations of a Kerr spacetime when
the spacetime metric is written in either ingoing or outgoing Kerr-Schild form.
We also write explicit formulae for setting up the initial data for the
Teukolsky equation in the time domain in terms of a three metric and an
extrinsic curvature. The motivation of this work is to have in place a
formalism to study the evolution in the ``close limit'' of two recently
proposed solutions to the initial value problem in general relativity that are
based on Kerr-Schild slicings. A perturbative formalism in horizon penetrating
coordinates is also very desirable in connection with numerical relativity
simulations using black hole ``excision''.
