In this paper we consider generalizations in 4 dimensions of the Einstein-Maxwell equations which typically arise from Kaluza-Klein theories. We specify conditions such that stationary solutions lead to non-linear σ-models for symmetric spaces. Using both this group theoretic structure and some properties of harmonic maps we are able to generalize many of the known existence and uniqueness theorems for black holes in Einstein-Maxwell theory to this more general setting.

Dimensional renormalization is defined in such a way that the renormalized action principle holds. It is shown that this leads to a minimal, additive renormalization. The derivation of Ward-Takahashi indentities and Callan-Symanzik equations from the action principle is exemplified.

We present analytical and numerical results for static, spherically symmetric solutions of the Einstein-Yang-Mills-Higgs equations corresponding to magnetic monopoles and non-abelian magnetically charged black holes. In the limit of in nite Higgs mass we give an existence proof for these solutions. The stability of the abelian extremal Reissner-Nordstr m black holes is reanalyzed.

We study the global behaviour of static, spherically symmetric solutions of the Einstein-Yang-Mills equations with gauge group SU(2). Our analysis results in three disjoint classes of solutions with a regular origin or a horizon. The 3-spaces (t = const.) of the first, generic class are compact and singular. The second class consists of an infinite family of globally regular, resp. black hole solutions. The third type is an oscillating solution, which although regular is not asymptotically flat.