Constructive procedure for perturbations of spacetimes

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Abstract
The method of Debye scalar superpotentials has previously been extended by the authors to curved spaces to yield a constructive procedure for neutrino, electromagnetic, and gravitational perturbations of algebraically special spacetimes. The solution of a decoupled scalar wave equation is differentiated to give the solution of the corresponding spinor or tensor perturbation field equations. In this paper covariant formulations and proofs are given. The results are derived in a general spinor formalism framework which extends earlier exterior differential form and tensor treatments of the electromagnetic case.

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