Renormalized charged scalar current on a Reissner-Nordström black hole in the presence of charge superradiance

We compute the renormalized charge current for a massless, minimally coupled, charged quantum scalar field on a charged Reissner-Nordström black hole space-time, using the method of pragmatic mode-sum renormalization. Since the field exhibits superradiance, we consider the past Unruh, Boulware and Candelas-Chrzanowski-Howard states and study how the renormalized current in these states depends on the charges of the black hole and scalar field. We also study the backreaction of the charge current on the electromagnetic field.