Killing tensors and conformal Killing tensors from conformal Killing vectors

Rani, Raffaele; Edgar, S. Brian; Barnes, Alan

doi:10.1088/0264-9381/20/11/301

Cited by 52 publications

(58 citation statements)

References 30 publications

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“…In general, if a metric d s 2 possesses a Killing-Stäckel tensor K µν , then for any conformally related metric ds 2 there is an induced conformal Killing-Stäckel tensor with components given by Q µν = K µν ; see e.g. [155]. In particular, the string frame Killing-Stäckel tensor induces a conformal Killing-Stäckel tensor for the Einstein frame metric.…”

Section: Killing Tensors and Separabilitymentioning

confidence: 99%

Black holes inN=8supergravity from SO(4,4) hidden symmetries

2014

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We detail the construction of the most general asymptotically flat, stationary, rotating, non-extremal, dyonic black hole of the four-dimensional N = 2 supergravity coupled to 3 vector multiplets that describes the ST U model. It generates through Udualities the most general asymptotically flat, stationary black hole of N = 8 supergravity. We develop the solution generating technique based on SO(4, 4)/SL(2, R) 4 coset model symmetries, with an emphasis on the 4-fold permutation symmetry of the gauge fields. We indicate how previously known non-extremal and extremal solutions of the ST U model are recovered as limiting cases. Several properties of the general black hole solution are discussed, including its thermodynamics, the quadratic mass formula, the Bogomolny-Prasad-Sommerfield limit, the slow and fast extremal rotating limits, its properties in regards to the Kerr/conformal field theory correspondence, its Killing tensors and the separability of geodesic motion and probe scalars.

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Section: Killing Tensors and Separabilitymentioning

confidence: 99%

Black holes inN=8supergravity from SO(4,4) hidden symmetries

2014

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“…The set of all CKV (respectively, SCKV, HKV and KV) form a finite dimensional Lie algebra denoted by C (respectively, S, H and G). Koutras [25] devised an algorithm to find KTs using CKVs and this algorithm was generalized by Rani, Edgar and Barnes [26], [27]: Given a pair of CKVs X, Y satisfying…”

Section: Introductionmentioning

confidence: 99%

Killing tensors in pp-wave spacetimes

Keane¹,

Tupper²

2010

Class. Quantum Grav.

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Abstract. The formal solution of the second order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.

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“…On the other hand, a class of irreducible Killing tensors that can be obtained from normal conformal Killing vectors. This last class has been considered by Koutras 19 and Rani et al 17 The results in the previous section allow us to give the canonical form for the metric tensors admitting irreducible Killing tensors of type 1 + (n − 1). Indeed, as the eigenstructure is integrable, the metric will be conformally related to a 1 + (n − 1) product metric.…”

Section: Ii) C V + D H Is a Killing Tensor C And D Being Arbitrary Cmentioning

confidence: 92%

On the geometry of Killing and conformal tensors

Coll

Ferrando

Sáez

2006

Journal of Mathematical Physics

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The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues, the condition to be a Killing or a conformal tensor is characterized in terms of its underlying almost-product structure. A canonical expression for the metrics admitting these kinds of symmetries is also presented. The space-time cases 1+3 and 2+2 are analyzed in more detail. Starting from this approach to Killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum Petrov-Bel type D solutions is offered. A generalization of these results to a wider family of type D space-times is also obtained.

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Killing tensors and conformal Killing tensors from conformal Killing vectors

Cited by 52 publications

References 30 publications

Black holes inN=8supergravity from SO(4,4) hidden symmetries

Black holes inN=8supergravity from SO(4,4) hidden symmetries

Killing tensors in pp-wave spacetimes

On the geometry of Killing and conformal tensors

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