Cosmological Pair Production of Charged and Rotating Black Holes

TL;DR

This paper explores the process of creating charged and rotating black hole pairs in a cosmological setting, using complex instantons and modified actions to understand their probabilities and thermodynamic properties.

Contribution

It introduces a classification of Kerr-Newman-deSitter spacetimes, constructs complex instantons for black hole pair creation, and modifies the action functional to account for rotation effects.

Findings

Derived creation probabilities consistent with black hole entropy.

Classified all relevant KNdS-type spacetimes.

Showed instantons are necessarily complex due to regularity.

Abstract

We investigate the general process of black hole pair creation in a cosmological background, considering the creation of charged and rotating black holes. We motivate the use of Kerr-Newmann-deSitter solutions to investigate this process, showing how they arise from more general C-metric type solutions that describe a pair of general black holes accelerating away from each other in a cosmological background. All possible KNdS-type spacetimes are classified and we examine whether they may be considered to be in full thermodynamic equilibrium. Instantons that mediate the creation of these space-times are constructed and we see that they are necessarily complex due to regularity requirements. Thus we argue that instantons need not always be real Euclidean solutions to the Einstein equations. Finally, we calculate the actions of these instantons and find that the standard action functional must be modified to correctly take into account the effects of the rotation. The resultant probabilities for the creation of the space-times are found to be real and consistent with the interpretation that the entropy of a charged and rotating black hole is the logarithm of the number of its quantum states.