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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.
We show that the nonlinear $sigma-$model in an asymptotically $AdS_3$ space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear $sigma-$model fields and minimally coupled to gravity. The local symmetry trans
In Einstein-Maxwell theory black holes are uniquely determined by their mass, their charge and their angular momentum. This is no longer true in Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N) Einstein-Yang-Mills black h
We revisit the physical effects of discrete $mathbb{Z}_p$ gauge charge on black hole thermodynamics, building on the seminal work of Coleman, Preskill, and Wilczek. Realising the discrete theory from the spontaneous breaking of an Abelian gauge theor
Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields in the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with sc
We construct and analyse Kerr black holes (BHs) with synchronised axionic hair. These are the BH generalisations of the recently constructed rotating axion boson stars arXiv:2005.05982. Such BHs are stationary, axially symmetric, asymptotically flat