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

Abstract

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 AdS2 near-horizon geometry which is fibered by the transverse spacetime directions. In this paper we allow for the most general fibration over AdS2 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 AdS4 electrically charged Kerr-Newman black hole in 4d $$ \mathcal{N} $$ 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.

M2-branes on Discs and Multi-Charged Spindles

“…Since the non-rotating Einstein-Maxwell solutions studied in [6] are a sub-class of the solutions studied here, one would expect that such a rotating solution is also possible for the multi-charge solutions with four charges. Such solutions would fit into the classification of [21] which studied the near-horizon of rotating black holes in M-theory. This would also allow for the possibility of spinning discs following the ideas presented in this paper on the different choices of global completions of the local solutions.…”

“…This would also allow for the possibility of spinning discs following the ideas presented in this paper on the different choices of global completions of the local solutions. Such a generalisation has been studied for rotating multi-charge D3-branes in [4] and it would be interesting to study the embedding of those solutions in the classification in [21].…”

“…Understanding how [21] seems to encompass both magnetic AdS and Kerr-Newmann AdS solutions is also of particular interest and may be used to generate new rotating solutions.…”

“…We would like to thank Eric Marcus for useful discussions and collaboration on [21]. CC thanks KIAS for their hospitality during the latter stages of this work and Niall Macpherson and Achilleas Passias for collaboration on [11].…”

On Type IIA AdS$_3$ solutions and massive GK geometries

“…In[76] similar types of condition for the Ricci scalar appears with a Laplacian like term. The geometries of[76] generalise GK geometries by including rotation, though this is not the origin of such a term here.…”