Explorations of four and five dimensional black hole spacetimes

Abstract

This thesis concentrates on four and five dimensional black holes and their associated geodesies. Some coordinate charts are presented, which are useful in the analysis of both static and rotating black holes, and their mathematical properties investigated before some methods of solving Einstein's vacuum field equations are examined. The Myers-Perry black hole metric is derived before going on to describe the Inverse Scattering Method of generating new vacuum solutions. The Inverse Scattering Method is used to generate the single and doubly spinning black ring metrics and then the physical properties of these solutions is explored in detail. The latter part of this thesis looks at different ways of visualising geodesies in various spacetimes and examines the pros and cons of each particular method, as well as looking at several examples of geodesies with different parameters. The geodesies of the singly spinning black ring are calculated and it is shown that they cannot in general be analytically integrated. In light of this, some restricted analytic scenarios are investigated with the intention of gaining some insight into how the geodesies behave in the spacetime as a whole. Finally, a method is presented which allows string charges to be added to any vacuum solution to Einstein's equations. The properties of this new charged solution are then compared with the neutral starting solution. The doubly spinning black ring is used as a model to demonstrate how the method can be used to charge up a specific black hole solution and the resulting thermodynamic properties of this charged doubly spinning black ring are then examined.