Abstract
In this paper we discuss the construction of conserved tensors (currents) involving conformal Killing-Yano tensors (CKYTs), generalising the corresponding constructions for Killing-Yano tensors (KYTs). As a useful preparation for this, but also of intrinsic interest, we derive identities relating CKYTs and geometric quantities. The behaviour of CKYTs under conformal transformations is also given, correcting formulae in the literature. We then use the identities derived to construct covariantly conserved “currents”. We find several new CKYT currents and also include a known one by Penrose which shows that “trivial” currents are also useful. We further find that rank-n currents based on rank-n CKYTs k must have a simple form in terms of dk. By construction, these currents are covariant under a general conformal rescaling of the metric. How currents lead to conserved charges is then illustrated using the Kerr-Newman and the C-metric in four dimensions. Separately, we study a rank-1 current, construct its charge and discuss its relation to the recently constructed Cotton current for the Kerr-Newman black hole.
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Acknowledgments
Ö.S. would like to thank D.O. Devecioğlu for help with xAct, and an austere and grim first referee who forced us to forge this paper into a more resilient form. The research of U.L. was supported in part by the 2236 Co-Funded Scheme2 (CoCirculation2) of TÜBİTAK (Project No:120C067).6 In addition, support from the Leverhulme trust is gratefully acknowledged by U.L.
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ArXiv ePrint: 2206.08037
Leverhulme Visiting Professor at Imperial College. (Ulf Lindström)
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Lindström, U., Sarıoğlu, Ö. Geometry, conformal Killing-Yano tensors and conserved “currents”. J. High Energ. Phys. 2023, 176 (2023). https://doi.org/10.1007/JHEP05(2023)176
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DOI: https://doi.org/10.1007/JHEP05(2023)176