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Killing spinors and gravitational perturbations

It is shown that in a vacuum space‐time, possibly with a nonzero cosmological constant, which admits a D(1,0) Killing spinor, one component of the perturbed Weyl spinor that satisfies a decoupled equation, when multiplied by an appropriate factor made out of the components of the Killing spinor, constitutes a Debye potential that generates metric perturbations of the considered background. It is also shown that in the case where the background is of type N, there is an operation that relates the gravitational perturbations and the zero‐rest‐mass fields of spin‐0, ‐ 1/2 , and ‐1.