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

TL;DR

This work classifies all near-horizon geometries of stationary extremal Einstein-Maxwell black holes with a nonpositive cosmological constant in four dimensions, showing that the non-static axisymmetric NH geometry uniquely corresponds to the Kerr-Newman family (including AdS4 when Λ<0), and static NHs reduce to AdS2×Σ with Σ of constant curvature. It establishes that the supersymmetric NH sector is a special subset with a simple entropy expression and identifies which physical quantities can be computed from NH data alone. The results provide strong evidence for a near-horizon/black-hole-uniqueness picture for extremal AdS4 black holes and clarify how horizon data constrain global charges; the entropy formula for the supersymmetric AdS4 black hole parallels known AdS5 results. Entropy is related to horizon area via $S = A/(4G)$, and specific relations among charges, angular momentum, and the cosmological constant emerge in the supersymmetric limit.

Abstract

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. Finally, we show which physical quantities of extremal black holes may be computed from the near-horizon limit alone, and point out a simple formula for the entropy of the known supersymmetric AdS(4) black hole. Analogous results are presented in the case of vanishing cosmological constant.