Hannover 2003 – wissenschaftliches Programm
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GR: Gravitation und Relativitätstheorie
GR 4: Klassische Allgemeine Relativit
ätstheorie
GR 4.2: Fachvortrag
Dienstag, 25. März 2003, 14:20–14:40, A310
Constructing Killing Tensors and Dual Geometries — •Raffaele Rani1, Brian Edgar2, and Alan Barnes3 — 1Theoretical Astrophysics, Institute of Astronomy adn Astrophysics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany — 2Department of Mathematics, Linköping University, 58183 Linköping, Sweden — 3School of Engineering & Applied Science, Aston University, Birmingham, B4 7ET, U.K.
Killing tensors are known to be a generalisation of Killing vectors and to be linked with integrals of motion and the theory of separation of variables. However not so many examples of them are known since to obtain them by direct solution of the Killing equations is in most cases a complicated task.
We here present three methods to construct Killing tensors from vectors and tensors possessing special properties. We first consider the case of Killing tensors constructed from conformal Killing vectors and then discuss the result that cofactor Killing tensors can always be constructed from non-singular special conformal Killing tensors. Finally, we introduce the concept of dual geometries, spaces obtained using Killing tensors as spacetime metrics.