Accelerating Black Holes and Spinning Spindles
Abstract
We study solutions in the Pleba\'nski--Demia\'nski 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 non-vanishing the D=4 black hole metrics have conical singularities. By uplifting the solutions to D=11 supergravity using a regular Sasaki-Einstein 7-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, WCP1[n-,n+], also known as a spindle, which is labelled 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 generalise 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 appropriate magnetic flux.