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

Understand

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.