The near-horizon geometry of supersymmetric rotating AdS4 black holes in M-theory

We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity which are associated to rotating M2-branes. Such rotating black holes admit an AdS(2) near-horizon geometry which is fibered by the transverse spacetime directions. In this paper we allow for the most general fibration over AdS(2) with a flux configuration permitting rotating M2-branes. Using G-structure techniques we rewrite the conditions for supersymmetry in terms of differential equations on an eight-dimensional balanced space. The 9d compact internal space is a U(1)-fibration over this 8d base. The geometry is constrained by a master equation reminiscent of the one found in the non-rotating case. We give a Lagrangian from which the equations of motion may be derived, and show how the asymptotically AdS(4) electrically charged Kerr-Newman black hole in 4d N = 2 supergravity is embedded in the classification. In addition, we present the conditions for the near-horizon geometry of rotating black strings in Type IIB by using dualities with the 11d setup.

Automated summary

We classify the necessary and sufficient conditions to obtain the near-horizon geometry of extremal supersymmetric rotating black holes embedded in 11d supergravity associated to rotating M2-branes. The conditions for supersymmetry are rewritten in terms of differential equations on an eight-dimensional balanced space using G-structure techniques. The geometry is constrained by a master equation reminiscent of the non-rotating case, and the asymptotically AdS(4) electrically charged Kerr-Newman black hole in 4d N = 2 supergravity is embedded in the classification. Additionally, the conditions for the near-horizon geometry of rotating black strings in Type IIB are presented using dualities with the 11d setup.