Geometry, conformal Killing-Yano tensors and conserved “currents”

Lindström U., Sarıoğlu B. Ö.

Journal of High Energy Physics, vol.2023, no.5, 2023 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2023 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.1007/jhep05(2023)176
  • Journal Name: Journal of High Energy Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH, Directory of Open Access Journals
  • Keywords: Classical Theories of Gravity, Differential and Algebraic Geometry
  • Middle East Technical University Affiliated: Yes


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.