End Point of the Ultraspinning Instability and Violation of Cosmic Censorship

We determine the end point of the axisymmetric ultraspinning instability of asymptotically flat Myers-Perry black holes in $D=6$ spacetime dimensions. In the nonlinear regime, this instability gives rise to a sequence of concentric rings connected by segments of black membrane on the rotation plane. The latter become thinner over time, resulting in the formation of a naked singularity in finite asymptotic time and hence a violation of the weak cosmic censorship conjecture in asymptotically flat higher-dimensional spaces.

Figure 1

Top: Embedding diagrams of the AH at different stages of the evolution of the ultraspinning instability of a MP BH with $a/{\mu }^{\frac{1}{3}}=1.7$. Here $\widehat{t}=t/{\mu }^{\frac{1}{3}}$. The structure of rings that form on the membrane in the middle depends sensitively on the grid setting and is not convergent [28]. Bottom: Normalized spacetime Kretschmann invariant pulled back onto the AH.

Figure 2

Top: Radial velocity $\dot{r}\equiv dr/dt$ of a null ray moving with the AH. Middle: Zoom of the thinnest region. The arrows indicate the direction of the local velocity of the rings. Bottom: Evolution of the AH thickness at several representative locations for $a/{\mu }^{\frac{1}{3}}=1.7$.