Rotating black holes with non-Abelian hair

TL;DR

This paper reviews rotating black holes with non-Abelian gauge fields, highlighting their non-uniqueness, induced electric charges, and various types of hair depending on the matter fields involved.

Contribution

It provides a comprehensive review of rotating black holes with non-Abelian hair, including effects of Higgs fields and dilaton coupling, extending previous static solutions.

Findings

Rotation induces electric charge in SU(2) Yang-Mills black holes.

Black holes can carry monopole or sphaleron hair depending on matter fields.

Inclusion of a dilaton leads to Smarr-type mass formulas.

Abstract

We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang-Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.