Scalar field perturbation on six-dimensional ultra-spinning black holes

TL;DR

The paper addresses the stability of six-dimensional ultra-spinning Myers-Perry black holes under massless scalar perturbations. By exploiting the separability of the scalar field equation in this background and solving for quasinormal modes via continued fractions, it computes the resonant frequencies $\omega$ and separation constants $A$. In the membrane limit and across several $(j,m,\ell)$ sectors, all computed modes satisfy ${\rm Im}(\omega) > 0$, showing no scalar-driven instability. The findings align with Cardoso, Siopsis and Yoshida and strengthen the conclusion that ultra-spinning higher-dimensional black holes are stable in the scalar sector, informing phenomenology of TeV-scale gravity scenarios.

Abstract

We have studied the scalar field perturbations on six-dimensional ultra-spinning black holes. We have numerically calculated the quasinormal modes of rotating black holes. Our results suggest that such perturbations are stable.

Figures (6)

• Figure 1: The quasinormal modes for $(j,m,\ell)=(0,0,0)$.
• Figure 2: The quasinormal modes for $(j,m,\ell)=(0,\pm1,0)$.
• Figure 3: The quasinormal modes for $(j,m,\ell)=(0,\pm2,0)$ and $(0,0,1)$.
• Figure 4: The quasinormal modes for $(j,m,\ell)=(0,\pm3,0)$ and $(0,\pm1,1)$.
• Figure 5: The quasinormal modes for $(j,m,\ell)=(0,\pm4,0)$, $(0,\pm2,1)$ and $(0,0,2)$.