Complex Instantons and Charged Rotating Black Hole Pair Creation

TL;DR

This paper investigates the pair-creation of charged rotating black holes using complex instantons, establishing a connection between black hole entropy and quantum states, and demonstrating the consistency of their probabilities.

Contribution

It introduces the use of complex instantons to describe the pair-creation process of charged rotating black holes, ensuring regularity and real probabilities.

Findings

Instantons describing pair-creation are necessarily complex.

Probabilities derived from these instantons are real and consistent.

Black hole entropy relates to the logarithm of quantum states.

Abstract

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.