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We present new soliton and hairy black hole solutions ofEinstein-non-Abelian-Proca theory in asymptotically anti-de Sitter space-timewith gauge group ${\mathfrak {su}}(2)$. For static, spherically symmetricconfigurations, we show that the gauge field must be purely magnetic, and solvethe resulting field equations numerically. The equilibrium gauge field isdescribed by a single function $\omega (r)$, which must have at least one zero.The solitons and hairy black holes share many properties with the correspondingsolutions in asymptotically flat space-time. In particular, all the solutionswe study are unstable under linear, spherically symmetric, perturbations of themetric and gauge field.

Solitons and hairy black holes in Einstein-non-Abelian-Proca theory in anti-de Sitter space-time