Rotating black holes must be axisymmetric

Hollands, Ishibashi, and Wald offer their proof that rotating black holes, even the higher-dimensional ones, must be axisymmetric. In other words, they always admit a "rotational" Killing vector field. You should realize that the horizon is not necessarily spherical anymore if the number of spacetime dimensions exceeds four. A previous blog text about higher-dimensional black holes' uniqueness and unusual topologies was here.