Complex Instantons and Charged Rotating Black Hole Pair Creation
  We consider the general process of pair-creation of charged rotating black holes. We find that instantons which describe this process are necessarily complex due to regularity requirements. However their associated probabilities are real, and fully consistent with the interpretation that the entropy of a charged rotating black hole is the logarithm of the number of its quantum states. 
I. S. Booth and R. B. Mann