Instability of Ultra-Spinning Black Holes

TL;DR

This work shows that in spacetime dimensions $d\ge 6$, ultra-spinning black holes with arbitrarily large angular momentum per mass develop a dynamical instability as the horizon becomes pancake-like in the rotation plane. By mapping the near-horizon geometry to a black membrane in a black-brane limit, the authors invoke the Gregory–Laflamme instability to argue that these solutions are unstable at large $a$, effectively yielding a higher-dimensional Kerr bound $J^{d-3}\lesssim \beta_d G M^{d-2}$. Thermodynamic arguments reinforce this instability, with a transition from Kerr-like to membrane-like behavior at a finite ratio $a/r_+$ and corresponding critical values of $a^{d-3}/\mu$. Entropy-based fragmentation scenarios further indicate instability thresholds at modest $a/r_+$, while the possibility of rippled-horizon black holes and multiple-spin generalizations emerges. In braneworld contexts, ultra-spinning black holes are unlikely to produce macroscopic violations of four-dimensional bounds, though they motivate rich phenomenology for microscopic higher-dimensional gravity.

Abstract

It has long been known that, in higher-dimensional general relativity, there are black hole solutions with an arbitrarily large angular momentum for a fixed mass. We examine the geometry of the event horizon of such ultra-spinning black holes and argue that these solutions become unstable at large enough rotation. Hence we find that higher-dimensional general relativity imposes an effective `Kerr-bound' on spinning black holes through a dynamical decay mechanism. Our results also give indications of the existence of new stationary black holes with `rippled' horizons of spherical topology. We consider various scenarios for the possible decay of ultra-spinning black holes, and finally discuss the implications of our results for black holes in braneworld scenarios.