Complex Metrics in the Gravitational Path Integral

When studying quantum gravity, one is sometimes led to consider complex metrics. These arise as saddle points of the Euclidean gravitational path integral. However, some complex metrics are pathological, therefore it is important to have criteria to distinguish the acceptable metrics from the unphysical ones. The thesis applies to different examples a criterion recently proposed by Witten. In particular, this will be applied to rotating, electrically charged supersymmetric black holes in Anti de Sitter space, which have attracted considerable attention recently in the context of holography.