• DOI:10.1007/s10714-016-2126-2
• Corpus ID: 113397042

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

@article{Baxter2016OnTG,
  title={On the global existence of hairy black holes and solitons in anti-de Sitter Einstein–Yang–Mills theories with compact semisimple gauge groups},
  author={J. Erik Baxter},
  journal={General Relativity and Gravitation},
  year={2016},
  volume={48},
  pages={1-43}
}

• J. Baxter
• Published 18 April 2016
• Mathematics
• General Relativity and Gravitation

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 $${\mathfrak {su}}(N)$$su(N) system. We find the analysis differs from the asymptotically flat case in some important ways: the biggest difference is that for $$\Lambda <0$$Λ<0, solutions are much less constrained as $$r\rightarrow \infty $$r→∞, 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 $$|\Lambda |\rightarrow \infty $$|Λ|→∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the $${\mathfrak {su}}(N)$$su(N) case proved important to stability.