Nonaxisymmetric instability of rapidly rotating black hole in five dimensions

Abstract

We present results from numerical solution of Einstein's equation in five dimensions describing evolution of rapidly rotating black holes. We show, for the first time, that the rapidly rotating black holes in higher dimensions are unstable against nonaxisymmetric deformation; for the five-dimensional case, the critical value of spin parameter for onset of the instability is $\approx 0.87$.

Figures (3)

• Figure 1: Evolution of deformation parameter $\eta$ for $a/\mu^{1/2}=0.80$--0.89.
• Figure 2: $h_+$ and its absolute value as functions of retarded time for $a/\mu^{1/2}=0.85$, 0.87, and 0.89 (dashed, long-dashed, and solid curves). $h_+$ is extracted for $r \sim \lambda$ where $\lambda$ is a gravitational-wave length.
• Figure 3: Characteristic frequency of gravitational waves as a function of $a/\mu^{1/2}$.