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

TL;DR

This paper explores the complex properties of 5D Einstein-Maxwell-Chern-Simons black holes, revealing phenomena like non-uniqueness, counterrotation, and negative horizon mass as the Chern-Simons coupling varies.

Contribution

It uncovers how varying the Chern-Simons coefficient leads to novel black hole behaviors, including counterrotation and negative horizon mass, highlighting the role of supersymmetry and stability boundaries.

Findings

Existence of counterrotating black holes with opposite horizon rotation and angular momentum.

Emergence of black holes with zero angular momentum but finite rotation.

Black holes with negative horizon mass while maintaining positive total mass.

Abstract

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.