Radially excited rotating black holes in Einstein-Maxwell-Chern-Simons theory

Rotating black holes in Einstein-Maxwell-Chern-Simons theory possess remarkable features, when the Chern-Simons coupling constant reaches a critical value. Representing single asymptotically flat black holes with horizons of spherical topology, they exhibit non-uniqueness. In particular, there even exist extremal and non-extremal black holes with the same sets of global charges. Both extremal and non-extremal black holes form sequences of radially excited solutions, that can be labeled by the node number of the magnetic gauge potential function. The extremal Reissner-Nordstr\"om solution is no longer always located on the boundary of the domain of existence of these black holes, and it neither remains the single extremal solution with vanishing angular momentum. Instead a whole sequence of rotating extremal $J=0$ solutions is present, whose mass converges towards the mass of the Reissner-Nordstr\"om solution. These radially excited extremal solutions are all associated with the same near horizon solution. Moreover, there are near horizon solutions that are not realized as global solutions.