Schwinger production rate between horizons in de Sitter black holes

Determine the Schwinger pair-production rate between the black hole horizon and the cosmological horizon for general Reissner–Nordström–de Sitter black holes, providing its spatial dependence and parameter scaling across the inter-horizon region.

Background

The paper computes the spatial profile of the Schwinger production rate for extremal Reissner–Nordström black holes in asymptotically flat spacetime using the worldline instanton approach, identifying the Compton wavelength as the characteristic scale and showing a near-horizon dominance.

Extending this analysis to de Sitter space is motivated by potential implications for the Weak Gravity Conjecture (WGC) in spacetimes with a cosmological horizon. However, the authors do not perform this computation and explicitly flag the determination of the rate between the black hole and cosmological horizons in general de Sitter black holes as an open problem.