Electromagnetic properties of Kerr–anti-de Sitter black holes

We examine the electromagnetic properties of Kerr–anti-de Sitter (Kerr-AdS) black holes in four and higher spacetime dimensions. Assuming that the black holes may carry a test electric charge we show that the Killing one-form which represents the difference between the timelike generators in the spacetime and in the reference background can be used as a potential one-form for the associated electromagnetic field. In four dimensions the potential one-form and the Kerr-AdS metric with properly rescaled mass parameter solve the Einstein-Maxwell equations, thereby resulting in the familiar Kerr-Newman-AdS solution. We solve the quartic equation governing the location of the event horizons of the Kerr-Newman-AdS black holes and present closed analytic expressions for the radii of the horizons. We also compute the gyromagnetic ratio for these black holes and show that it corresponds to $g=2$ just as for ordinary black holes in asymptotically flat spacetime. Next, we compute the gyromagnetic ratio for the Kerr-AdS black holes with a single angular momentum and with a test electric charge in all higher dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio of the rotation parameter to the curvature radius of the AdS background. At the critical limit, when the boundary Einstein universe is rotating at the speed of light, it tends to $g=2$ irrespective of the spacetime dimension. Finally, we consider the case of a five-dimensional Kerr-AdS black hole with two angular momenta and show that it possesses two distinct gyromagnetic ratios in accordance with its two orthogonal two-planes of rotation. In the special case of two equal angular momenta, the two gyromagnetic ratios merge into one leading to $g=4$ at the maximum angular velocities of rotation.