Quasi-normal modes of a multi-dimensional rotating Kerr black hole

The aim of this paper is to present a general way to calculate quasi-normal modes (QNM) of the Teukolsky equation for higher dimensional (d > 4) Kerr spacetime with compactified extra dimensions. In order to do so, we develop a formalism derived from spinors: we call it multispinor formalism. It is based on vectors of two-spinors and permits us to develop a formalism analogous to that of Newman-Penrose in 4d. From this we show how to derive the Teukolsky equation for gravitational perturbations and calculate the QNM. In order to keep calculations simple we fix, as an example, the dimension number to be six, but the work can be readily generalized to other spacetime dimensions.