Quantum Hair on Black Holes

TL;DR

This paper explores quantum hair on black holes, revealing two types of exponentially decaying hair linked to discrete gauge charge and color magnetic charge, affecting black hole properties through virtual flux tubes.

Contribution

It introduces detailed semi-classical calculations of quantum hair effects, distinguishes primary and secondary hair, and examines their implications for black hole thermodynamics and quantum numbers.

Findings

Quantum hair can be associated with discrete gauge charge and color magnetic charge.

Effects of discrete gauge charge are non-perturbative in ar.

Color magnetic charge effects become ar-independent in certain limits.

Abstract

A black hole may carry quantum numbers that are {\it not} associated with massless gauge fields, contrary to the spirit of the ``no-hair'' theorems. We describe in detail two different types of black hole hair that decay exponentially at long range. The first type is associated with discrete gauge charge and the screening is due to the Higgs mechanism. The second type is associated with color magnetic charge, and the screening is due to color confinement. In both cases, we perform semi-classical calculations of the effect of the hair on local observables outside the horizon, and on black hole thermodynamics. These effects are generated by virtual cosmic strings, or virtual electric flux tubes, that sweep around the event horizon. The effects of discrete gauge charge are non-perturbative in $\hbar$, but the effects of color magnetic charge become $\hbar$-independent in a suitable limit. We present an alternative treatment of discrete gauge charge using dual variables, and examine the possibility of black hole hair associated with discrete {\it global} symmetry. We draw the distinction between {\it primary} hair, which endows a black hole with new quantum numbers, and {\it secondary} hair, which does not, and we point out some varieties of secondary hair that occur in the standard model of particle physics.