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We present weighted covariant derivatives and wave operators forperturbations of certain algebraically special Einstein spacetimes in arbitrarydimensions, under which the Teukolsky and related equations become weightedwave equations. We show that the higher dimensional generalization of theprincipal null directions are weighted conformal Killing vectors with respectto the modified covariant derivative. We also introduce a modified Laplace-deRham-like operator acting on tensor-valued differential forms, and show thatthe wave-like equations are, at the linear level, appropriate projections {\emoff shell} of this operator acting on the curvature tensor; the projectiontensors being made out of weighted conformal Killing-Yano tensors. We give offshell operator identities that map the Einstein and Maxwell equations intoweighted scalar equations, and using adjoint operators we construct solutionsof the original field equations in a compact form from solutions of thewave-like equations. We study the extreme and zero boost weight cases; extremeboost corresponding to perturbations of Kundt spacetimes (which includes NearHorizon Geometries of extreme black holes), and zero boost to static blackholes in arbitrary dimensions. In 4 dimensions our results apply to Einsteinspacetimes of Petrov type D and make use of weighted Killing spinors.

Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes