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.

• Received 23 December 1991

DOI:https://doi.org/10.1103/PhysRevD.45.2762