The specific nonlinear vector $sigma$-model coupled to Einstein gravity is investigated. The model arises in the studies of the gravitating matter in non-commutative geometry. The static spherically symmetric spacetimes are identified by direct solving of the field equations. The asymptotically flat black hole with the ``non-commutative vector hair appears for the special choice of the integration constants, giving thus another counterexample to the famous ``no-hair theorem.
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