Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes

Understand

We consider stationary extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions.

• We determine all non-static axisymmetric near-horizon geometries (with non-toroidal horizon topology) and all static near-horizon geometries for black holes of this kind.
• This allows us to deduce that the most general near-horizon geometry of an asymptotically globally AdS(4) rotating extremal black hole, is the near-horizon limit of extremal Kerr-Newman-AdS(4).
• We also identify the subset of near-horizon geometries which are supersymmetric.