Microstates of accelerating and supersymmetric AdS${}_4$ black holes from the spindle index

We provide a first principles derivation of the microscopic entropy of a very general class of supersymmetric, rotating and accelerating black holes in AdS${}_4$. This is achieved by analysing the large-$N$ limit of the spindle index and completes the construction of the first example of a holographic duality involving supersymmetric field theories defined on orbifolds with conical singularities.