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 but that hyperspherically symmetric black holes can be constructed numerically in generalized Einstein‐Yang‐Mills models. 5‐dimensional black strings with horizon topology 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.
- Black holes
- Gauge field theory
- Black hole thermodynamics
- Higher dimensional black holes
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