Abelian Higgs Hair for AdS-Schwarzschild Black Hole

TL;DR

This paper demonstrates that Abelian Higgs vortex solutions can exist as hair on AdS-Schwarzschild black holes, showing how scalar fields can form stable configurations around black holes and affect spacetime geometry.

Contribution

It introduces vortex line solutions of the Abelian Higgs field in AdS-Schwarzschild backgrounds and explores their role as black hole hair, including gravitational effects.

Findings

Black holes can support Abelian Higgs vortex solutions as hair.

The vortex solutions induce a deficit angle in the black hole spacetime.

Numerical analysis confirms the existence of these solutions as stable configurations.

Abstract

We show that the Abelian Higgs field equations in the background of the four dimensional AdS-Schwarzschild black hole have a vortex line solution. This solution, which has axial symmetry, is a generalization of the AdS spacetime Nielsen-Olesen string. By a numerical study of the field equations, we show that black hole could support the Abelian Higgs field as its Abelian hair. Also, we conside the self gravity of the Abelian Higgs field both in the pure AdS spacetime and AdS-Schwarzschild black hole background and show that the effect of string as a black hole hair is to induce a deficit angle in the AdS-Schwarzschild black hole.