Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions | Zendy

Pavel Krtouš | Zendy; David Kubizňák | Zendy; Don N. Page | Zendy; Valeri P. Frolov | Zendy

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Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Author(s) -

Pavel Krtouš,

David Kubizňák,

Don N. Page,

Valeri P. Frolov

Publication year - 2007

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2007/02/004

Subject(s) - mathematical physics , spacetime , geodesic , physics , constant of motion , tensor (intrinsic definition) , rank (graph theory) , killing vector field , equations of motion , mathematics , mathematical analysis , classical mechanics , pure mathematics , quantum mechanics , combinatorics

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensionalspacetime with such a principal Killing-Yano tensor, we show how to generatek=[(D+1)/2] Killing-Yano tensors, of rank D-2j for all j=0,...,k-1, and krank-2 Killing tensors, giving k constants of geodesic motion that are ininvolution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) withits principal Killing-Yano tensor (gr-qc/0610144), these constants and theconstants from the k Killing vectors give D independent constants ininvolution, making the geodesic motion completely integrable (hep-th/0611083).The constants of motion are also related to the constants recently obtained inthe separation of the Hamilton-Jacobi and Klein-Gordon equations(hep-th/0611245).Comment: 7 page

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