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

TL;DR

This paper explores radially excited rotating black holes in Einstein-Maxwell-Chern-Simons theory, revealing non-uniqueness, sequences of solutions, and complex extremal behaviors influenced by the Chern-Simons coupling.

Contribution

It uncovers the existence of radially excited black hole solutions with non-uniqueness and complex extremal structures in Einstein-Maxwell-Chern-Simons theory.

Findings

Existence of radially excited solutions labeled by magnetic gauge potential nodes.

Sequences of extremal and non-extremal black holes with identical global charges.

Presence of near horizon solutions not realized globally.

Abstract

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.