Einstein-Yang-Mills black holes in anti de-Sitter space

In this thesis we consider Einstein-Yang-Mills black holes in asymptotically anti-de Sitter space, in the presence of an su(N) gauge �eld. For a purely magnetic gauge �eld we de�ne a set of charges, namely the mass and N - 1 gauge invariant magnetic charges, and show that they characterize stable black holes.

We then go on to consider dyonic black holes which carry both electric and magnetic charge. We investigate spherically symmetric black holes and solitons, and �nd equations of motion for solutions with su(N) gauge �elds. These equations are solved numerically to �nd black hole and soliton solutions with su(2) and su(3) gauge groups.

We then turn to dyonic black holes with planar event horizons and investigate their suitability as gravitational analogues to high temperature superconductors under the AdS/CFT correspondence. We generalise a previously known ansatz for su(2) gauge groups to su(N), and show that there is a critical temperature above which non-abelian solutions do not exist. Below this critical temperature, we show that they are thermodynamically favoured over equivalent Reissner-Nordstr�om solutions, and have in�nite D.C. conductivity.