Charged quantum scalar expectation values on charged black holes

In this thesis we extend the current methods for calculating renormalized expectation values of observables for neutral quantum scalar fields on curved spacetimes to charged quantum scalar fields. We then use these methods to numerically calculate expectation values for massive and massless charged scalar fields on the Reissner-Nordstr¨om spacetime in a variety of quantum states. This includes calculations in both the presence and absence of charge superradiance. We also use our results for the massless field to discuss the backreaction of the charged quantum field on the electromagnetic field.