Accelerating black holes and spinning spindles

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