Monodromy Approach to Pair Production of Charged Black Holes and Electric Fields

TL;DR

This paper develops a monodromy method to analyze pair production, absorption cross sections, and quasi-normal modes in black hole and electric field backgrounds, offering a new practical approach for studying these phenomena.

Contribution

It introduces a monodromy-based technique for calculating pair production and related quantities in various black hole and electric field scenarios, extending previous methods.

Findings

Monodromy method successfully computes pair production rates.

Results agree with exact hypergeometric function solutions.

Method shows potential for general black hole and electromagnetic field analysis.

Abstract

To find the pair production, absorption cross section and quasi-normal modes in background fields, we advance the monodromy method that makes use of the regular singular points of wave equations. We find the mean number of pairs produced in background fields whose mode equations belong to the Riemann differential equation and apply the method to the three particular cases: (i) charges near the horizon of near-extremal black holes, (ii) charges with minimal energy under the static balance in nonextremal charged black holes, and (iii) charges in the Sauter-type electric fields. We then compare the results from the monodromy with those from the exact wave functions in terms of the hypergeometric functions with three regular singular points. The explicit elaboration of monodromy and the model calculations worked out here seem to reveal evidences that the monodromy may provide a practical technique to study the spontaneous pair production in general black holes and electromagnetic fields.