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

We compute pair production rate of charged black holes in de Sitter space in four dimensional Einstein-Maxwell theory with 4-derivative corrections. We find that the probability measure of producing a pair of generic dyonically charged black holes is still given by the sum of two entropies, one of which is associated with the black hole outer horizon and the other is associated with the cosmological horizon. Specializing to examples of smooth configurations, 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.Comment: 29 pages, 2 figure