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We consider the general process of pair-creation of charged rotating blackholes. We find that instantons which describe this process are necessarilycomplex due to regularity requirements. However their associated probabilitiesare real, and fully consistent with the interpretation that the entropy of acharged rotating black hole is the logarithm of the number of its quantumstates.Comment: 11 pages, 1 figure, Latex, text shortened with only minor changes in  content, accepted for Phys Rev Letter

Complex Instantons and Charged Rotating Black Hole Pair Creation