Vacuum polarisation on asymptotically anti-de Sitter spacetimes

This thesis considers a real, massless, conformally coupled scalar field propagating on the covering space of four-dimensional anti-de Sitter space (CadS) and on four-dimensional Schwarzschild-anti de Sitter space (SadS). Numerical results for the vacuum polarisation are obtained in CadS with Robin conditions imposed at the boundary. A proof is given to demonstrate that results approach the same finite limit at the boundary unless Dirichlet conditions are imposed. Numerical results for the vacuum polarisation are obtained in SadS with Dirichlet conditions imposed at the boundary, using the extended coordinates method of renormalisation. These results are then extended for Robin boundary conditions, where we see qualitatively similar behaviour to that observed in CadS.