2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35430The specific nonlinear vector $σ$-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.10 pages, LaTeX, PRA-HEP-93/9General Relativity and Quantum CosmologyHigh Energy Physics - Theorytext