Multicharge accelerating black holes and spinning spindles

We construct a family of multidyonically charged and rotating supersymmetric AdS2×Σ solutions of D=4, N=4 gauged supergravity, where Σ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS4 that we conjecture to exist. We demonstrate this in the nonrotating limit, constructing the accelerating black hole solutions and showing that the nonspinning spindle solutions arise as the near horizon limit of the supersymmetric and extremal subclass of these black holes. From the near horizon solutions we compute the Bekenstein-Hawking entropy of the black holes as a function of the conserved charges, and show that this may equivalently be obtained by extremizing a simple entropy function. For appropriately quantized magnetic fluxes, the solutions uplift on S7, or its N=4 orbifolds S7/Γ, to smooth supersymmetric solutions to D=11 supergravity, where the entropy is expected to count microstates of the theory on N M2-branes wrapped on a spinning spindle, in the large N limit.