Abstract
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 Geroch–Held–Penrose formalism, of decoupled field equations for the linearized Weyl scalars for all spin weights and identify the gauge source functions occurring 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.
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