Vortices and extreme black holes: The question of flux expulsion - art. no. 084022

It has been claimed that extreme black holes exhibit a phenomenon of Bur ex pulsion for Abelian Higgs vortices, irrespective of the relative width of t he vortex to the black hole. Recent work by two of the authors showed a sub tlety in the treatment of the event horizon, which cast doubt on this claim . We analyze in detail the vortex-extreme black hole system, showing that, while flux expulsion can occur, it does not do so in ail cases. We give ana lytic proofs for both expulsion and penetration of flux, in each case deriv ing a bound for that behavior. We also present extensive numerical work bac king up, and refining. these claims, and showing in detail how a vortex can end on a black hole in all situations. We also calculate the back reaction of the vortex on the geometry, and comment on the more general vortex-blac k hole system. [S0556-2821(99)04608-1].