Non-Axisymmetric Instability of Rotating Black Holes in Higher Dimensions

Abstract

We calculate the scalar-gravitational quasi-normal modes of equal angular momenta Myers-Perry black holes in odd dimensions. We find a new bar-mode (non-axisymmetric) classical instability for $D \ge 7$. These black holes were previously found to be unstable to axisymmetric perturbations for spins very near extremality. The bar-mode instability we find sets in at much slower spins, and is therefore the dominant instability of these black holes. This instability has important consequences for the phase diagram of black holes in higher dimensions.

Figures (2)

• Figure 1: Plot of $\text{Im}(\omega)$ for for the dominantly unstable mode, $(\kappa,m) = (0,2)$. The black points at $a=0$ were computed using a different code based upon the gauge invariant formalism of Ref Kodama:2003jz. Note that as $D$ increases the critical spin for which $\text{Im}(\omega) = 0$ decreases. For $D=5$, $\text{Im}(\omega) \rightarrow 0^-$ as $a/a_{\text{ext}} \rightarrow 1$, and we find no instability. The inset plot zooms the region where $\text{Im}(\omega)$ becomes positive.
• Figure 2: Plot of $\text{Re}(\omega)$ for for the dominantly unstable mode, $(\kappa,m) = (0,2)$. The black points at $a=0$ were computed using a different code based upon the gauge invariant formalism of Ref Kodama:2003jz.