Note on Rotating Charged Black Holes in Einstein-Maxwell-Chern-Simons Theory

TL;DR

This paper presents a simplified Kerr-Schild framework for rotating charged black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory, introduces new solutions for slow rotation with arbitrary Chern-Simons coupling, and computes their physical properties.

Contribution

It provides a new Kerr-Schild type description for known solutions and derives novel slow rotation solutions for arbitrary Chern-Simons coefficients, along with their mass, angular momenta, and gyromagnetic ratios.

Findings

Simplified Kerr-Schild description of known solutions.

New analytic slow rotation solutions for arbitrary Chern-Simons coupling.

Explicit formulas for mass, angular momenta, and gyromagnetic ratios.

Abstract

We show that the general solution of Chong, Cvetic, Lu and Pope for nonextremal rotating charged black holes in five-dimensional minimal gauged supergravity, or equivalently in the Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and with the Chern-Simons coefficient $ \nu=1 $, admits a simple description in a Kerr-Schild type framework with two scalar functions. Next, assuming this framework as an ansatz, we obtain new analytic solutions for slowly rotating charged black holes in the Einstein-Maxwell-Chern-Simons theory with $ \nu\neq 1 .$ Using a covariant superpotential derived from Noether identities within the Katz-Bicak-Lynden-Bell approach, we calculate the mass and angular momenta for the general supergravity solution as well as for the slowly rotating solution with two independent rotation parameters. For the latter case, we also calculate the gyromagnetic ratios and obtain simple analytic formulas, involving both the parameters of the black holes and the Chern-Simons coefficient.