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

TL;DR

This paper introduces a multispinor formalism to compute quasi-normal modes of higher-dimensional Kerr black holes, extending existing methods to spacetimes with extra dimensions.

Contribution

It develops a novel multispinor formalism based on vectors of two-spinors for calculating QNM in higher-dimensional Kerr spacetimes, generalizable beyond six dimensions.

Findings

Derived the Teukolsky equation for gravitational perturbations in 6D Kerr spacetime.

Demonstrated the formalism's applicability to higher dimensions with potential for generalization.

Provided a method to calculate QNM for multi-dimensional rotating black holes.

Abstract

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.