Abstract

We study the axially symmetric static solitons of the O(3) nonlinear $\ensuremath{\sigma}$ model coupled to (2+1)-dimensional anti--de Sitter gravity. The obtained solutions are not self-dual under a static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged $\mathrm{Ba}\mathrm{n}\ifmmode \tilde{}\else \~{}\fi{}\mathrm{ados}$-Teitelboim-Zanelli black holes without non-Abelian scalar hair.

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