Instabilities of extremal rotating black holes in higher dimensions

Understand

Recently, Durkee and Reall have conjectured a criterion for linear instability of rotating, extremal, asymptotically Minkowskian black holes in $d\ge 4$ dimensions, such as the Myers-Perry black holes.

• They considered a certain elliptic operator, $\cA$, acting on symmetric trace-free tensors intrinsic to the horizon.
• Based in part on numerical evidence, they suggested that if the lowest eigenvalue of this operator is less than the critical value $-1/4$ ( called "effective BF-bound"), then the black hole is linearly unstable.
• In this paper, we prove an extended version of their conjecture.