Accelerating black holes and spinning spindles

We study solutions in the Plebański-Demiański family which describe an accelerating, rotating, and dyonically charged black hole in AdS4. 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, SE7, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the D=11 solutions incorporate an SE7 fibration over a two-dimensional weighted projective space, WCP[n-,n+]1, 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 AdS2×Y9 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.