Rotating black holes and black bars at large D

We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions D. The basic idea is that an asymptotically flat black brane evolving under the Gregory-Laflamme instability forms lumps that closely resemble a localized black hole. In this manner, the large-D effective equations for extended black branes can be used to study localized black holes. We show that these equations have exact solutions for black-hole-like lumps on the brane, which correctly capture the main properties of Schwarzschild and Myers-Perry black holes at large D, including their slow quasinormal modes and the ultraspinning instabilities (axisymmetric or not) at large angular momenta. Furthermore, we obtain a novel class of rotating ‘black bar’ solutions, which are stationary when D → ∞, and are long-lived when D is finite but large, since their gravitational wave emission is strongly suppressed. The leading large D approximation reproduces to per-cent level accuracy previous numerical calculations of the bar-mode growth rate in D = 6, 7.