Accelerating black holes and spinning spindles

Abstract

We study solutions in the Plebański–Demiański family which describe an accelerating, rotating, and dyonically charged black hole in AdS 4 . These are solutions of D = 4 Einstein-Maxwell theory with a negative cosmological constant and hence minimal D = 4 gauged supergravity. It is well known that when the acceleration is nonvanishing the D = 4 black hole metrics have conical singularities. By uplifting the solutions to D = 11 supergravity using a regular Sasaki-Einstein seven-manifold, S E 7 , we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the D = 11 solutions incorporate an S E 7 fibration over a two-dimensional weighted projective space, W C P 1 [ n − , n + ] , also known as a spindle, which is labeled by two integers that determine the conical singularities of the D = 4 metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric AdS 2 × Y 9 solutions of D = 11 supergravity, which generalize a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain N = 2 , d = 3 quiver gauge theories compactified on a spinning spindle with the appropriate magnetic flux.