Charged rotating black holes in odd dimensions

We consider charged rotating black holes of Einstein–Maxwell theory in D=2N+1 dimensions, D⩾5. These black holes are asymptotically flat and possess a regular horizon of spherical topology. While they generically possess N independent angular momenta, associated with N distinct planes of rotation, we here focus on black holes with equal-magnitude angular momenta. In that case the angular dependence can be treated explicitly, and the field equations reduce to a system of 5 ordinary differential equations, which depend on the dimension. We solve these equations numerically in D=5, 7 and 9 dimensions. We discuss the global and horizon properties of these black holes, as well as their extremal limits.