Non-abelian black holes and black strings in higher dimensions

TL;DR

This paper reviews higher-dimensional non-abelian black hole solutions, highlighting the non-existence of hyperspherical black holes in more than four dimensions, the construction of numerical solutions, and the properties of black strings, including their deformation and stability.

Contribution

It introduces the existence of deformed non-abelian black strings and analyzes their thermodynamic instability, expanding understanding of higher-dimensional black objects.

Findings

Hyperspherically symmetric black holes do not exist in dimensions greater than four.

Numerical solutions for hyperspherically symmetric black holes are constructed.

Deformed non-abelian black strings are identified and shown to be thermodynamically unstable.

Abstract

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-Mills models. 5-dimensional black strings with horizon topology S^2 x S^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.