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We consider the possibility of deriving a decoupled equation in terms of Weyltensor components for gravitational perturbations of theSchwarzschild-Tangherlini solution. We find a particular gauge invariantcomponent of the Weyl tensor does decouple and argue that this corresponds tothe vector modes of Ishibashi and Kodama. Also, we construct a Hertz potentialmap for solutions of the electromagnetic and gravitational perturbationequations of a higher dimensional Kundt background using the decoupled equationof Durkee and Reall. Motivated by recent work of Guica and Strominger, we usethis to construct the asymptotic behaviour of metric perturbations of thenear-horizon geometry of the 5d cohomogeneity-1 Myers-Perry black hole.

The perturbation theory of higher dimensional spacetimes a la Teukolsky