Vortex hair on AdS black holes

TL;DR

This paper investigates vortex hair on charged rotating AdS black holes, revealing interactions with horizons, boundary extensions, and phase transitions, with implications for holography and the Meissner effect.

Contribution

It provides analytical and numerical analysis of vortex hair on AdS black holes, including phase transition characteristics and boundary behavior, advancing understanding of black hole hair in holographic contexts.

Findings

Vortex interacts with black hole horizon and boundary.

Meissner effect causes flux expulsion in extremal black holes.

Phase transition is first order with rotation, second order without.

Abstract

We analyse vortex hair for charged rotating asymptotically AdS black holes in the abelian Higgs model. We give analytical and numerical arguments to show how the vortex interacts with the horizon of the black hole, and how the solution extends to the boundary. The solution is very close to the corresponding asymptotically flat vortex, once one transforms to a frame that is non-rotating at the boundary. We show that there is a Meissner effect for extremal black holes, with the vortex flux being expelled from sufficiently small black holes. The phase transition is shown to be first order in the presence of rotation, but second order without rotation. We comment on applications to holography.