Conformal Yano–Killing tensor for the Kerr metric and conserved quantities

Jezierski, Jacek; Łukasik, Maciej

doi:10.1088/0264-9381/23/9/008

Cited by 35 publications

(53 citation statements)

References 51 publications

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“…In particular, in vacuum (e = g = Λ = 0) we recover the KY tensor for the Kerr metric (l = 0), respectively for the NUT solution (a = 0) studied recently in [116], respectively [115].…”

Section: A22 Generalized Black Holessupporting

confidence: 52%

“…In 1993, Gibbons et al demonstrated that due to the presence of Killing-Yano tensor the classical spinning particles in this background possess enhanced worldline supersymmetry [91]. Conserved quantities in the Kerr geometry generated by f were discussed in 2006 by Jezierski and Łukasik [116].…”

Section: 4)mentioning

confidence: 99%

“…6 It allows us to use the theorem (see, e.g., [219], [116]) which states that whenever k is a CKY tensor for the metric g then Ω 3 k is a CKY tensor for the conformally rescaled metric Ω 2 g. This would justify the transition from the known KY tensor (A.76) to the CKY tensor (A.46), up to the fact, that in the transition from (A.42) to (A.74) we also need to change metric functions P (p) and Q(r). Fortunately, as mentioned above, the 'universality' of k, i.e., the property that (A.76) remains KY tensor for the metric (A.74) with arbitrary function P (p) and Q(r), can be demonstrated.…”

Section: A23 Carter's Metricmentioning

confidence: 99%

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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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“…In particular, in vacuum (e = g = Λ = 0) we recover the KY tensor for the Kerr metric (l = 0), respectively for the NUT solution (a = 0) studied recently in [116], respectively [115].…”

Section: A22 Generalized Black Holessupporting

confidence: 52%

Section: 4)mentioning

confidence: 99%

Section: A23 Carter's Metricmentioning

confidence: 99%

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Hidden Symmetries of Higher-Dimensional Rotating Black Holes

2007

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“…[13]). It turns out that, although Y and * Y are different tensors, the forms F (R, Y ) and F (R, * Y ) are the same.…”

Section: Introductionmentioning

confidence: 99%

Conformal Yano–Killing tensors for the Taub–NUT metric

Jezierski

Łukasik²

2007

Class. Quantum Grav.

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“…(4). Then T is proper (non-Killing, equivalently, + p 0) conformal Killing if and only if M is shear-free, vorticity-free, and and p are differentially related to the expansion and acceleration through Eq.…”

mentioning

confidence: 99%

Perfect fluid space-times whose energy-momentum tensor is conformal Killing

Sharma¹,

Ghosh²

2010

Journal of Mathematical Physics

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A full description of the integrability condition for the twistor equation in curved space-times and new wave equations for conformally invariant spinor fieldsWe show that the energy-momentum tensor T of an expanding perfect fluid spacetime ͑M , g͒ is a nontrivial conformal Killing tensor if and only if M is shear-free, vorticity-free, and satisfies certain energy and force equations. In particular, if T is conformal Killing, we show that the perfect fluid is stationary and its energydensity and pressure are constant.

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Conformal Yano–Killing tensor for the Kerr metric and conserved quantities

Cited by 35 publications

References 51 publications

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Conformal Yano–Killing tensors for the Taub–NUT metric

Perfect fluid space-times whose energy-momentum tensor is conformal Killing

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