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On the existence of soliton and hairy black hole solutions of {\mathfrak {su}}(N) Einstein–Yang–Mills theory with a negative cosmological constant
We study the existence of soliton and black hole solutions of four-dimensional Einstein–Yang–Mills theory with a negative cosmological constant. We prove the existence of non-trivial solutions for any integer N, with N − 1 gauge field degrees of freedom. In particular, we prove the existence of solutions in which all …