Non-abelian black holes and black strings in higher dimensions

We review the properties of static, higher dimensional black hole solutions in theories where non-abelian gauge fields are minimally coupled to gravity. It is shown that black holes with hyperspherically symmetric horizon topology do not exist in d > 4, but that hyperspherically symmetric black holes can be constructed numerically in generalized Einstein-Yang-M ills models. 5-dimensional black strings with horizon topology S(2)xS(1) are also discussed. These are so-called undeformed and deformed non-abelian black strings, which are translationally invariant and correspond to 4-dimensional non-abelian black holes trivially extended into one extra dimensions. The fact that black strings can be deformed, i.e. axially symmetric for constant values of the extra coordinate is a new feature as compared to black string solutions of Einstein (-Maxwell) theory. It is argued that these non-abelian black strings are thermodynamically unstable.