Abelian Higgs hair for extreme black holes and selection rules for snapping strings

Abstract

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 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. We discuss the implications for strings that end at black holes, as in processes where a string snaps by nucleating black holes.

4 pages REVTeX plus 3 figures. Additional figures and mpeg movies available at http://www.damtp.cam.ac.uk/user/ats25/strhole.html This paper is a condensed version of gr-qc/9706004, and is essentially the talk presented at The Eighth Marcel Grossmann Meeting on General Relativity, 22-27 June 1997, The Hebrew University, Jerusalem, Israel

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