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 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→ ∞, 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 | → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the su(N) case proved important to stability.