On the global existence of spherically symmetric hairy black holes and solitons in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

Abstract

We investigate the existence of black hole and soliton solutions to four dimensional, anti-de Sitter (adS), Einstein-Yang-Mills theories with general semisimple connected and simply connected gauge groups, concentrating on the so-called "regular" case. We here generalise results for the asymptotically flat case, and compare our system with similar results from the well-researched adS $\mathfrak{su}(N)$ system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for $\Lambda <0$, solutions are much less constrained as $r\to \infty$, making it possible to prove the existence of global solutions to the field equations in some neighbourhood of existing trivial solutions, and in the limit of $|\Lambda |\to \infty$. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the $\mathfrak{su}(N)$ case proved important to stability.

52 pages. arXiv admin note: text overlap with arXiv:gr-qc/0008042 by other authors

References in corpus (3)

• Abundant stable gauge field hair for black holes in anti-de Sitter space
• On the existence of soliton and hairy black hole solutions of su(N) Einstein-Yang-Mills theory with a negative cosmological constant
• On the existence of topological hairy black holes in $\mathfrak{su}(N)$ EYM theory with a negative cosmological constant

Cited by in corpus (3)

• Black Hole Entropy and Soft Hair
• Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective
• On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups