Non-uniqueness, Counterrotation, and Negative Horizon Mass of Einstein-Maxwell-Chern-Simons Black Holes

Stationary black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory possess surprising properties. When considering the Chern-Simons coefficient $\lambda$ as a parameter, two critical values of $\lambda$ appear: the supergravity value $\lambda_{\rm SG}=1$, and the value $\lambda=2$. At $\lambda=1$, supersymmetric black holes with vanishing horizon angular velocity, but finite angular momentum exist. As $\lambda$ increases beyond $\lambda_{\rm SG}$ a rotational instability arises, and counterrotating black holes appear, whose horizon rotates in the opposite sense to the angular momentum. Thus supersymmetry is associated with the borderline between stability and instability. At $\lambda=2$ rotating black holes with vanishing angular momentum emerge. Beyond $\lambda=2$ black holes may possess a negative horizon mass, while their total mass is positive. Charged rotating black holes with vanishing gyromagnetic ratio appear, and black holes are no longer uniquely characterized by their global charges.