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In the asymptotically AdS case, in addition to these solutions there exist singular solutions containing a BTZ black hole, but they are always hairless. There are no black hole vortex solutions. In the asymptotically flat case, we find that non-singular vortices round off the singularity of the point particle’s metric in 3 dimensions, whereas singular solutions consist of vortices holding a conical singularity at their core. We study the self-gravitating Abrikosov vortex in curved space with and with-out a (negative) cosmological constant, considering both singular and non-singular solutions with an eye to hairy black holes.
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