Black rings with a small electric charge: gyromagnetic ratios and algebraic alignment

TL;DR

This paper investigates electromagnetic fields around vacuum black rings, revealing their gyromagnetic ratios, flux expulsion properties, and algebraic classifications, highlighting differences from spherical black holes and extending understanding of higher-dimensional spacetimes.

Contribution

It provides the first detailed analysis of electromagnetic properties and algebraic types of charged black rings, including gyromagnetic ratios and flux behavior in extremal limits.

Findings

Gyromagnetic ratio g=3 for slightly charged black rings.

Black rings in extremal limit expel magnetic flux.

Charged black rings are algebraically general (type G) in higher dimensions.

Abstract

We study electromagnetic test fields in the background of vacuum black rings using Killing vectors as vector potentials. We consider both spacetimes with a rotating S^1 and with a rotating S^2 and we demonstrate, in particular, that the gyromagnetic ratio of slightly charged black rings takes the value g=3 (this will in fact apply to a wider class of spacetimes). We also observe that a S^2-rotating black ring immersed in an external "aligned" magnetic field completely expels the magnetic flux in the extremal limit. Finally, we discuss the mutual alignment of principal null directions of the Maxwell 2-form and of the Weyl tensor, and the algebraic type of exact charged black rings. In contrast to spherical black holes, charged rings display new distinctive features and provide us with an explicit example of algebraically general (type G) spacetimes in higher dimensions. Appendix A contains some global results on black rings with a rotating 2-sphere. Appendix C shows that g=D-2 in any D>=4 dimensions for test electromagnetic fields generated by a time translation.