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 re-scaled 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 2-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 .