Quantum corrections to pair production of charged black holes in de Sitter space

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.

Automated summary

We compute the Euclidean action of charged de Sitter black holes in the four-dimensional gravitational Euler-Heisenberg model, and find that it is controlled by the total entropy contributed by the black hole outer horizon and the cosmological horizon. The Euclidean action can be interpreted as the black hole production rate in de Sitter space for smooth configurations. We also observe that the 4-derivative couplings break the symmetry between the production rate of purely electric black holes and purely magnetic black holes, but electromagnetic duality induces a transformation on these couplings, mapping the physical quantities of one type of black hole to the other type while preserving the unitarity constraints.