Can extreme black holes have (long) Abelian Higgs hair?

It has been argued that a black hole horizon can support the long range fields of a Nielsen-Olesen string, and that one can think of such a vortex as black hole ``hair''. We show that the fields inside the vortex are completely expelled from a charged black hole in the extreme limit (but not in the near extreme limit). This would seem to imply that a vortex cannot be attached to an extreme black hole. Furthermore, we provide evidence that it is energetically unfavourable for ...

It is argued that an electronically charged dilaton black hole can support a long range field of a Nielsen-Olesen string. Combining both numerical and perturbative techniques we examine the properties of an Abelian-Higgs vortex in the presence of the black hole under consideration. Allowing the black hole to approach extremality we found that all fields of the vortex are expelled from the extreme black hole. In the thin string limit we obtained the metric of a conical electri...

We find evidence for the existence of solutions of the Einstein and Abelian Higgs field equations describing a black hole pierced by a Nielsen-Olesen vortex. This situation falls outside the scope of the usual no-hair arguments due to the non-trivial topology of the vortex configuration and the special properties of its energy-momentum tensor. By a combination of numerical and perturbative techniques we conclude that the black hole horizon has no difficulty in supporting the ...

It has been argued that the extremal dilaton black holes exhibit a flux expulsion of Abelian-Higgs vortices. We re-examine carefully the problem and give analytic proofs for the flux expulsion always takes place. We also conduct numerical analysis of the problem using three initial data sets on the horizon of an extreme dilatonic black hole, namely, core, vacuum and sinusoidal initial conditions. We also show that an Abelian-Higgs vortex can end on the extremal dilaton black ...

We study the problem of vortex solutions in the background of rotating black holes in both asymptotically flat and asymptoticlly anti de Sitter spacetimes. We demonstrate the Abelian Higgs field equations in the background of four dimensional Kerr, Kerr-AdS and Reissner-Nordstrom-AdS black holes have vortex line solutions. These solutions, which have axial symmetry, are generalization of the Nielsen-Olesen string. By numerically solving the field equations in each case, we fi...

We study the problem of vortex solutions in the background of an electrically charged black string. We show numerically that the Abelian Higgs field equations in the background of a four-dimensional black string have vortex solutions. These solutions which have axial symmetry, show that the black string can support the Abelian Higgs field as hair. This situation holds also in the case of the extremal black string. We also consider the self-gravity of the Abelian Higgs field a...

It has been claimed that extreme black holes exhibit a phenomenon of flux expulsion for abelian Higgs vortices, irrespective of the relative width of the vortex to the black hole. Recent work by two of the authors showed a subtlety in the treatment of the event horizon, which cast doubt on this claim. We analyse in detail the vortex/extreme black hole system, showing that while flux expulsion can occur, it does not do so in all cases. We give analytic proofs for both expulsio...

Behaviour of Dirac fermions in the background of a charged black string penetrated by an Abelian Higgs vortex is elaborated. One finds the evidence that the system under consideration can support fermion fields acting like a superconducting cosmic string in the sence that a nontrivial Dirac fermion field can be carried by the system in question. The case of nonextremal and extremal black string vortex systems were considered. The influence of electric and Higgs charge, the wi...

A Kerr black hole sporting cosmic string hair is studied in the context of the abelian Higgs model vortex. It is shown that a such a system displays much richer phenomenology than its static Schwarzschild or Reissner--Nordstrom cousins, for example, the rotation generates a near horizon electric field. In the case of an extremal rotating black hole, two phases of the Higgs hair are possible: Large black holes exhibit standard hair, with the vortex piercing the event horizon. ...

We studied, both analytically and numerically, an Abelian Higgs vortex in the spacetime of stationary axisymmetric black hole being the solution of the low-energy limit of the heterotic string theory, acted as hair on the black hole background. Taking into account the gravitational backreaction of the vortex we show that its influence is far more subtle than causing only a conical defect. As a consequence of its existence, we found that the ergosphere was shifted as well as e...