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Absence of Abelian Higgs Hair for Extreme Black Holes
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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 unfavorable for a thin vortex to interact with a large extreme black hole. This dispels the notion that a black hole can support long Abelian Higgs hair in the extreme limit.
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CHAMBLIN, A., et al. Absence of Abelian Higgs Hair for Extreme Black Holes. Physical Review Letters. 1998. Vol. 80, num. 20, pags. 4378-4381. ISSN 0031-9007. [consulted: 3 of August of 2026]. Available at: https://hdl.handle.net/2445/13245