Quantum Corrections to Pair Production of Charged Black Holes in de Sitter Space

TL;DR

This paper calculates quantum corrections to the pair production rate of charged black holes in de Sitter space, revealing how higher-derivative couplings affect electric-magnetic asymmetry and duality.

Contribution

It provides the first detailed analysis of quantum corrections to black hole pair production in de Sitter space within the Euler-Heisenberg model, highlighting symmetry breaking and duality transformations.

Findings

4-derivative couplings break electric-magnetic symmetry

Duality transformation maps electric to magnetic black holes

Unitarity constraints remain invariant under duality

Abstract

We compute Euclidean action of charged de Sitter black holes in four dimensional gravitational Euler-Heisenberg model. It turns out that the action of a general Euclidean dyonically charged black hole is still controlled by the total entropy contributed by the black hole outer horizon and the cosmological horizon. For smooth configurations, the Euclidean action can be interpreted as the black hole production rate in de Sitter space. We show that the 4-derivative couplings break the symmetry between the production rate of the purely electric black hole and that of the purely magnetic black hole. Although electromagnetic duality is no longer a symmetry, it induces a transformation on the 4-derivative couplings, mapping the physical quantities of a purely electric black hole to those of a purely magnetic black hole and vice versa. We also observe that under the same transformation, unitarity constraints on the 4-derivative couplings remain invariant.