The perturbation theory of higher-dimensional spacetimes in the manner of Teukolsky

We consider the possibility of deriving a decoupled equation in terms of Weyl tensor components for gravitational perturbations of the Schwarzschild-Tangherlini solution. We find that a particular gauge invariant component of the Weyl tensor does decouple and argue that this corresponds to the vector modes of Ishibashi and Kodama. Also, we construct a Hertz potential map for solutions of the electromagnetic and gravitational perturbation equations of a higher-dimensional Kundt background using the decoupled equation of Durkee and Reall. Motivated by the recent work of Guica and Strominger, we use this to construct the asymptotic behaviour of metric perturbations of the NHG of the 5D cohomogeneity-1 Myers-Perry black hole. (paper)