  In this paper we consider the field equations for linearized gravity and
other integer spin fields on the Kerr spacetime, and more generally on
spacetimes of Petrov type D. We give a derivation, using the GHP formalism, of
decoupled field equations for the linearized Weyl scalars for all spin weights
and identify the gauge source functions occuring in these. For the spin weight
0 Weyl scalar, imposing a generalized harmonic coordinate gauge yields a
generalization of the Regge-Wheeler equation. Specializing to the Schwarzschild
case, we derive the gauge invariant Regge-Wheeler and Zerilli equation directly
from the equation for the spin 0 scalar.
