Extremal Charged Rotating Black Holes in Odd Dimensions

TL;DR

This paper develops a perturbative method to construct extremal charged rotating black holes in odd dimensions within Einstein-Maxwell-Chern-Simons theory, revealing universal features of their gyromagnetic ratio and physical properties.

Contribution

It introduces a third-order perturbation approach starting from Myers-Perry solutions to analyze charged rotating black holes with Chern-Simons terms in odd dimensions.

Findings

Gyromagnetic ratio deviates from D-2 value due to charge corrections.

First correction to g/(D-2) is universal across dimensions.

Physical properties depend on charge and Chern-Simons coupling.

Abstract

Employing higher order perturbation theory, we obtain charged rotating black holes in odd dimensions, where the Einstein-Maxwell Lagrangian may be supplemented with a Chern-Simons term. Starting from the Myers-Perry solutions, we use the electric charge as the perturbative parameter, and focus on extremal black holes with equal-magnitude angular momenta. For Einstein-Maxwell-Chern-Simons theory with arbitrary Chern-Simons coupling constant, we perform the perturbations up to third order for any odd dimension. We discuss the physical properties of these black holes and study their dependence on the charge. In particular, we show that the gyromagnetic ratio $g$ of Einstein-Maxwell black holes differs from the lowest order perturbative value $D-2$, and that the first correction term to $g/(D-2)$ is universal.