Vortices and extreme black holes: the question of flux expulsion

TL;DR

This paper investigates whether flux expulsion occurs for abelian Higgs vortices around extreme black holes, providing analytic and numerical evidence that flux can both be expelled or penetrate, depending on conditions.

Contribution

It offers a detailed analysis showing flux expulsion is not universal, with analytic bounds and numerical simulations clarifying the vortex-black hole interaction.

Findings

Flux expulsion is not guaranteed in all cases.

Analytic bounds for vortex flux behavior are derived.

Numerical simulations support the analytic results.

Abstract

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 expulsion and penetration of flux, in each case deriving a bound for that behaviour. We also present extensive numerical work backing 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 backreaction of the vortex on the geometry, and comment on the more general vortex-black hole system.