Rotating black holes pierced by a cosmic string

A rotating black hole threaded by an infinitely long cosmic string is studied in the framework of the Abelian Higgs model. We show that contrary to a common belief, in the presence of rotation the backreaction of the string does not induce a simple conical deficit. This leads to new distinct features of the Kerr--string system such as modified ISCO or shifted ergosphere, though these effects are likely outside the range of observational precision. For an extremal rotating black hole, the system exhibits a first-order phase transition for the gravitational Meissner effect: whereas the horizon of large black holes is pierced by the vortex, small black holes exhibit a flux-expelled solution, with the gauge and scalar field remaining identically in their false vacuum state on the event horizon. A brief review prepared for the MG14 Proceedings.