Entropy of four-dimensional rotating BPS black hole dyons

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The known BPS dyon black hole solutions of the $N=4$ heterotic string in four dimensions with a nonzero angular momentum all have naked singularities. We show that it is possible to modify a certain class of these solutions by the addition of massive Kaluza-Klein fields in such a way that the solutions decompactify near the core to five-dimensional black hole solutions with regular event horizons. We argue that the degeneracy of the four-dimensional BPS dyon states is given, for large charges, by the five-dimensional geometric entropy.