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

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

2006-09-14

arxiv.org/abs/gr-qc/0609049v2

JHEP0612:054,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 3 figures. v2: new appendix C finds the gyromagnetic ratio g=D-2 in any dimensions, two new references. To appear in

Scientific paper

10.1088/1126-6708/2006/12/054

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.

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