Euclidean Black Hole Vortices

TL;DR

This paper demonstrates the existence of vortex solutions at black hole horizons in Euclidean spacetime, analyzing their properties and effects on black hole thermodynamics through numerical methods.

Contribution

It introduces new vortex solutions at black hole horizons in Euclidean spacetime and explores their impact on the geometry and thermodynamics of black holes.

Findings

Vortex solutions exist at black hole horizons in Euclidean spacetime.

Vortices modify the Schwarzschild geometry by effectively removing a slice.

Implications for black hole thermodynamics are discussed.

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 behaviours, 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 backreaction shows that the effect of the vortex is to cut a slice out of the Euclidean Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.