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.