Geometry, conformal Killing-Yano tensors and conserved “currents”
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 re...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2023)176 |
| _version_ | 1797736513601011712 |
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| author | Ulf Lindström Özgür Sarıoğlu |
| author_facet | Ulf Lindström Özgür Sarıoğlu |
| author_sort | Ulf Lindström |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T13:13:57Z |
| format | Article |
| id | doaj.art-e2701591bd644acfa7518e4b029f2801 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T13:13:57Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e2701591bd644acfa7518e4b029f28012023-08-27T11:06:08ZengSpringerOpenJournal of High Energy Physics1029-84792023-05-012023511510.1007/JHEP05(2023)176Geometry, conformal Killing-Yano tensors and conserved “currents”Ulf Lindström0Özgür Sarıoğlu1Department of Physics, Faculty of Arts and Sciences, Middle East Technical UniversityDepartment of Physics, Faculty of Arts and Sciences, Middle East Technical UniversityAbstract 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.https://doi.org/10.1007/JHEP05(2023)176Classical Theories of GravityDifferential and Algebraic Geometry |
| spellingShingle | Ulf Lindström Özgür Sarıoğlu Geometry, conformal Killing-Yano tensors and conserved “currents” Journal of High Energy Physics Classical Theories of Gravity Differential and Algebraic Geometry |
| title | Geometry, conformal Killing-Yano tensors and conserved “currents” |
| title_full | Geometry, conformal Killing-Yano tensors and conserved “currents” |
| title_fullStr | Geometry, conformal Killing-Yano tensors and conserved “currents” |
| title_full_unstemmed | Geometry, conformal Killing-Yano tensors and conserved “currents” |
| title_short | Geometry, conformal Killing-Yano tensors and conserved “currents” |
| title_sort | geometry conformal killing yano tensors and conserved currents |
| topic | Classical Theories of Gravity Differential and Algebraic Geometry |
| url | https://doi.org/10.1007/JHEP05(2023)176 |
| work_keys_str_mv | AT ulflindstrom geometryconformalkillingyanotensorsandconservedcurrents AT ozgursarıoglu geometryconformalkillingyanotensorsandconservedcurrents |