On the global existence of 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 Λ <0, solutions are much less constrained as r→ 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 |Λ |→ 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.
- Publication:
-
General Relativity and Gravitation
- Pub Date:
- October 2016
- DOI:
- 10.1007/s10714-016-2126-2
- arXiv:
- arXiv:1604.05012
- Bibcode:
- 2016GReGr..48..133B
- Keywords:
-
- Hairy black holes;
- Solitons;
- Semisimple gauge group;
- Anti-de Sitter;
- Einstein-Yang-Mills theory;
- Existence;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 52 pages. arXiv admin note: text overlap with arXiv:gr-qc/0008042 by other authors