Conformal Killing-Yano tensors for the Plebański-Demiański family of solutions

Kubizňák, David; Krtouš, Pavel

doi:10.1103/physrevd.76.084036

Cited by 69 publications

(64 citation statements)

References 50 publications

(94 reference statements)

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“…For example, by relaxing some of the conditions on the PCKY tensor the authors of [109], [108] were able to find 'generalized Kerr-NUT-(A)dS spacetimes'. Similarly, by generalizing our (unsuccessful) procedure of rescaling the Kerr-NUT-(A)dS metric [155] (see also Appendix C.6), new five-dimensional black hole solutions were recently obtained [169], [170].…”

Section: When the Einstein Equations With The Cosmological Constant Amentioning

confidence: 99%

“…The first section plays the role of an introduction for newcomers to the field where, on the well known 4D case, we illustrate the main ideas of the more complicated higher-dimensional theory developed in Parts I and II of this thesis. In the second section, based on [155], we discuss hidden symmetries for the Plebański-Demiański family of type D solutions.…”

Section: Appendix a On Hidden Symmetries In 4dmentioning

confidence: 99%

“…2 Here we demonstrate that also the attempt to 'accelerate' Kerr-NUT-(A)dS spacetime in a way analogous to 4D, i.e., by a conformal rescaling (cf. Appendix A.2), generally fails [155].…”

Section: C5 Integrability Of Some Functions In Kerr-nut-(a)ds Spacetmentioning

confidence: 99%

“…In this section, based on [155], we present explicit expressions for the conformal Killing-Yano tensors for the Plebański-Demiański family of type D solutions. Some physically important special cases are discussed in more detail.…”

Section: A2 Cky Tensors For the Plebański-demiański Class Of Solutionsmentioning

confidence: 99%

“…The thesis is based on the following published papers in peer reviewed journals: [77], [153], [193], [85], [148], [149], [155], [154], [78], [52], [151].…”

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Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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In this thesis we study higher-dimensional rotating black holes. Such black holes are widely discussed in string theory and brane-world models at present.We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime, describing the general rotating higher-dimensional asymptotically (anti) de Sitter black hole with NUT parameters, is in many aspects similar to its fourdimensional counterpart. Namely, we show that it admits a fundamental hidden symmetry associated with the principal conformal Killing-Yano tensor. Such a tensor generates towers of hidden and explicit symmetries. The tower of Killing tensors is responsible for the existence of irreducible, quadratic in momenta, conserved integrals of geodesic motion. These integrals, together with the integrals corresponding to the tower of explicit symmetries, make geodesic equations in the Kerr-NUT-(A)dS spacetime completely integrable. We further demonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, and stationary string equations allow complete separation of variables and the problem of finding parallel-propagated frames reduces to the set of the first order ordinary differential equations. Moreover, we show that the Kerr-NUT-(A)dS spacetime is the most general Einstein space which possesses all these properties. We also explicitly derive the most general (off-shell) canonical metric admitting the principal conformal Killing-Yano tensor and demonstrate that such a metric is necessarily of the special algebraic type D of the higher-dimensional algebraic classification. The results presented in this thesis describe the new and complete picture of the relationship of hidden symmetries and rotating black holes in higher dimensions. PrefaceWhen in 1963 Kerr discovered an astrophysically relevant but relatively complicated metric describing the gravitational field of a rotating black hole, it seemed that no analytical predictions were possible even for the simplest particle geodesic motion. However, a 'miracle' happened, and it turned out that not only the geodesic motion can be analytically solved, but also the equations describing various perturbations of this background can be 'drastically' simplified. This opened a way for studying astrophysical processes, such as the plasma accretion around black holes, the radiation produced by infalling matter, the origin of jets, the production and propagation of waves produced in the vicinity of black holes, and it even led to estimates of the gravitational wave production in star collisions and galaxy merges. It also facilitated the study of more theoretical problems, such as the problem of stability of the Kerr solution, the calculation of the quasinormal modes, or the study of the Hawking radiation. A hidden symmetry responsible for this miracle can be mathematically described by a simple antisymmetric object, called the Killing-Yano tensor.Recently, higher-dimensional rotating black hole spacetimes have become of high interest due to various developments in gravity and high energy physic...

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Section: When the Einstein Equations With The Cosmological Constant Amentioning

confidence: 99%

Section: Appendix a On Hidden Symmetries In 4dmentioning

confidence: 99%

“…2 Here we demonstrate that also the attempt to 'accelerate' Kerr-NUT-(A)dS spacetime in a way analogous to 4D, i.e., by a conformal rescaling (cf. Appendix A.2), generally fails [155].…”

Section: C5 Integrability Of Some Functions In Kerr-nut-(a)ds Spacetmentioning

confidence: 99%

Section: A2 Cky Tensors For the Plebański-demiański Class Of Solutionsmentioning

confidence: 99%

“…The thesis is based on the following published papers in peer reviewed journals: [77], [153], [193], [85], [148], [149], [155], [154], [78], [52], [151].…”

mentioning

confidence: 99%

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Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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Hidden Symmetries of the Type D Metrics

Breton,

Acevedo

2023

Trends in Mathematics

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Killing-Yano Cotton currents

Lindström

Sarıoğlu

2022

J. High Energ. Phys.

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We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). We consider the corresponding charges generally and then exemplify with the four-dimensional Plebański-Demiański metric where they are proportional to the sum of the squares of the electric and the magnetic charges. As part of the derivation, we also find the two conformal Killing-Yano tensors of the Plebański-Demiański metric in the recently introduced coordinates of Podolsky and Vratny. The construction of asymptotic charges for the Cotton current is elucidated and compared to the three-dimensional construction in Topologically Massive Gravity. For the three-dimensional case, we also give a conformal superspace multiplet that contains the Cotton current in the bosonic sector. In a mathematical section, we derive potentials for the currents, find identities for conformal KYTs and for KYTs in torsionful backgrounds.

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Conformal Killing-Yano tensors for the Plebański-Demiański family of solutions

Cited by 69 publications

References 50 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of the Type D Metrics

Killing-Yano Cotton currents

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