Euclidean black-hole vortices

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Abstract
We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviors, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an Abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the back reaction shows that the effect of the vortex is to cut a slice out of the Euclidean Schwarzschild geometry. The consequences of these solutions for black-hole thermodynamics are discussed.
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