Scalar perturbations of higher dimensional rotating and ultra-spinning black holes

TL;DR

The study investigates the stability of higher-dimensional rotating Kerr black holes against scalar perturbations, focusing on six dimensions and encompassing both low and ultra-spinning regimes. It combines a separation-of-variables formulation with Leaver’s continued-fraction method to compute quasinormal modes and, where possible, provides analytical WKB-type results in the Schwarzschild and ultra-spinning limits. The main finding is that the six-dimensional Kerr black hole with a single rotation parameter remains stable to scalar perturbations even as $a/r_H$ becomes very large, with $\mathrm{Im}(\omega_{QN})>0$ across studied modes and overtones. These results constrain possible new instabilities in higher dimensions and motivate future work on gravitational perturbations and related black-brane instabilities in the ultra-spinning regime.

Abstract

We investigate the stability of higher dimensional rotating black holes against scalar perturbations. In particular, we make a thorough numerical and analytical analysis of six-dimensional black holes, not only in the low rotation regime but in the high rotation regime as well. Our results suggest that higher dimensional Kerr black holes are stable against scalar perturbations, even in the ultra-spinning regime.

Figures (2)

• Figure 1: Real part of the fundamental QN frequency as a function of the rotation parameter $a$ for some $l\,,j\,,m$ values. The maximum is reached at zero rotation, and as $a$ increases the real part of $\omega_{QN}$ decreases monotonically.
• Figure 2: