Classification of Euclidean signature metrics admitting a rank 2 closed conformal Killing-Yano tensor
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Bibliographic record
Abstract
In this thesis, we start with a review of topics such as Lie derivatives, Killing vectors, and Killing tensors, as well as the generalizations of these objects to their conformal variants.We then introduce the form of the Kerr-NUT-(A)dS metric for an arbitrary number of dimensions, followed by a review and proof of a result by Houri, Oota, and Yasui.The main takeaway from this result is that if a metric of Euclidean signature, satisfying the Einstein equations, admits a rank 2 closed conformal Killing-Yano tensor, then it must be a member of the Kerr-NUT-(A)dS family of metrics.At the end, more recent work done by Frolov, Krtous, and Kubiznak is briefly mentioned, where a new family of metrics (not of Euclidean signature) is found to admit a principal tensor; a non-degenerate rank 2 closed conformal Killing-Yano tensor.This leads to the belief that the classification of metrics which admit these types of Killing-Yano tensors is far from complete.i 1 Introduction 1 2 Preliminaries: Killing vectors and tensors 3 2.1 The Lie derivative . . . . . . . . . . . . . .
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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