Infinitely Coloured Black Holes

TL;DR

This paper develops a framework for spherically symmetric black holes in an infinite gauge symmetry setting, exploring solutions relevant to string theory and holography, with implications for quantum decoherence.

Contribution

It formulates the field equations for $SU( olinebreak ext{infinity})$ Einstein-Yang-Mills theory and finds new black hole solutions with infinite gauge hair.

Findings

Solutions simplify with negative cosmological constant

Black holes have infinite gauge field hair

Relevance to holography and AdS/CFT

Abstract

We formulate the field equations for $SU(\infty)$ Einstein-Yang-Mills theory, and find spherically symmetric black-hole solutions. This model may be motivated by string theory considerations, given the enormous gauge symmetries which characterize string theory. The solutions simplify considerably in the presence of a negative cosmological constant, particularly for the limiting cases of a very large cosmological constant or very small gauge field. The situation of an arbitrarily small gauge field is relevant for holography and we comment on the AdS/CFT conjecture in this light. The black holes possess infinite amounts of gauge field hair, and we speculate on possible consequences of this for quantum decoherence, which, however, we do not tackle here.