Aspects of quantum charged scalar field theory in curved spacetime: Black hole superradiance and Hadamard renormalisation

This thesis investigates the behaviour of charged scalar fields on curved background spacetimes. In Part I of this thesis, a brief review of quantum field theory in Schwarzschild spacetime is given.
In Part II, the Reissner-Nordström solution is introduced, before a massless, minimally-coupled charged scalar field is introduced and its dynamics on this spacetime are studied. The field is then quantised via canonical quantisation and various quantum states are defined in analogue with quantum states in Schwarzschild spacetime. This part concludes with analytical and numerical investigations of the expectation values of observables in various states.
In Part III, a charged scalar field of arbitrary mass and scalar coupling to the curvature is considered in a general background spacetime. The Hadamard renormalisation procedure is then developed for each of the three cases of two dimensions, an even number of dimensions and an odd number of dimensions. The renormalisation counterterms required for the evaluation of the RSET are derived explicitly. This part concludes with a discussion of the renormalisation ambiguities associated with Hadamard renormalisation.