The perturbation theory of higher dimensional spacetimes a la Teukolsky

TL;DR

This paper explores decoupled equations for gravitational perturbations in higher-dimensional black hole spacetimes, identifying gauge-invariant components and constructing Hertz potential maps, advancing understanding of perturbation behavior near black hole horizons.

Contribution

It derives a decoupled Weyl tensor component for higher-dimensional black holes and constructs a Hertz potential framework for perturbations in these spacetimes, extending previous methods.

Findings

Identified a gauge-invariant Weyl tensor component that decouples in higher dimensions.

Constructed a Hertz potential map for electromagnetic and gravitational perturbations.

Analyzed the asymptotic behavior of metric perturbations near the horizon of a 5D Myers-Perry black hole.

Abstract

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 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 recent work of Guica and Strominger, we use this to construct the asymptotic behaviour of metric perturbations of the near-horizon geometry of the 5d cohomogeneity-1 Myers-Perry black hole.