Rotating black holes in higher dimensional Einstein-Maxwell gravity

The strategy of obtaining the familiar Kerr-Newman solution in general relativity is based on either using the metric ansatz in the Kerr-Schild form, or applying the method of complex coordinate transformation to a nonrotating charged black hole. In practice, this amounts to an appropriate rescaling of the mass parameter in the metric of uncharged black holes. Using a similar approach, we assume a special metric ansatz in $N+1$ dimensions and present a new analytic solution to the Einstein-Maxwell system of equations. It describes rotating charged black holes with a single angular momentum in the limit of slow rotation. We also give the metric for a slowly rotating charged black hole with two independent angular momenta in five dimensions. Finally, we compute the gyromagnetic ratio of these black holes which corresponds to the value $g=N\ensuremath{-}1$.

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