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

TL;DR

This paper classifies all possible near-horizon geometries of extremal rotating AdS(4) black holes, showing they are uniquely determined by the extremal Kerr-Newman-AdS(4) solution and identifying supersymmetric cases.

Contribution

It provides a complete classification of near-horizon geometries for extremal AdS(4) black holes, including static, non-static, and supersymmetric cases, and derives a simple entropy formula.

Findings

Most general near-horizon geometry is that of extremal Kerr-Newman-AdS(4).

Identified subset of supersymmetric near-horizon geometries.

Derived a simple formula for the entropy of supersymmetric AdS(4) black holes.

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.