We consider charged rotating black holes in D = 2N + 1 dimensions, D ≥ 5. While these black holes generically possess N independent angular momenta, associated with N distinct planes of rotation, we here focus on black holes with equal-magnitude angular momenta. The angular dependence can then be treated explicitly, and a system of 5 D-dependent ordinary differential equations is obtained. We solve these equations numerically for Einstein-Maxwell theory in D = 5, 7 and 9 dimensions. We discuss the global and horizon properties of these black holes, as well as their extremal limits.

We consider charged rotating black holes in 5-dimensional Einstein-Maxwell theory. These black holes are asymptotically flat, they possess a regular horizon of spherical topology and two independent angular momenta associated with two distinct planes of rotation. We discuss their global and horizon properties, and derive a generalized Smarr formula. We construct these black holes numerically, focussing on black holes with a single angular momentum, and with two equalmagnitude angular momenta.

We construct exact charged rotating black holes in Einstein-Maxwell-dilaton theory in D spacetime dimensions, D ≥ 5, by embedding the D dimensional Myers-Perry solutions in D + 1 dimensions, and performing a boost with a subsequent Kaluza-Klein reduction. Like the Myers-Perry solutions, these black holes generically possess N = [(D − 1)/2] independent angular momenta. We present the global and horizon properties of these black holes, and discuss their domains of existence.

We construct rotating hairy black holes in SU͑2͒ Einstein-Yang-Mills theory. These stationary axially symmetric black holes are asymptotically flat. They possess non-trivial non-Abelian gauge fields outside their regular event horizon, and they carry non-Abelian electric charge. In the limit of vanishing angular momentum, they emerge from the neutral static spherically symmetric Einstein-Yang-Mills black holes, labeled by the node number of the gauge field function. With increasing angular momentum and mass, the non-Abelian electric charge of the solutions increases, but remains finite. The asymptotic expansion for these black hole solutions includes noninteger powers of the radial variable.

5-dimensional Einstein-Maxwell-Chern-Simons theory with Chern-Simons coefficient λ = 1 has supersymmetric black holes with vanishing horizon angular velocity, but finite angular momentum. Here supersymmetry is associated with a borderline between stability and instability, since for λ > 1 a rotational instability arises, where counterrotating black holes appear, whose horizon rotates in the opposite sense to the angular momentum. For λ > 2 black holes are no longer uniquely characterized by their global charges, and rotating black holes with vanishing angular momentum appear.