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A '''Killing tensor''', named after [[Wilhelm Killing]], is a symmetric [[tensor]], known in the theory of [[general relativity]], <math>K</math> that satisfies | |||
:<math> \nabla_{(\alpha}K_{\beta\gamma)} = 0 \,</math> | |||
where the parentheses on the indices refer to the [[symmetric tensor|symmetric part]]. | |||
This is a generalization of a [[Killing vector]]. While Killing vectors are associated with continuous symmetries (more precisely, differentiable), and hence very common, the concept of Killing tensor arises much less frequently. The [[Kerr metric|Kerr solution]] is the most famous example of a [[semi-Riemannian manifold|manifold]] possessing a Killing tensor. | |||
==See also== | |||
*[[Killing form]] | |||
*[[Killing vector field]] | |||
*[[Wilhelm Killing]] | |||
[[Category:Riemannian geometry]] | |||
Latest revision as of 18:01, 18 December 2013
A Killing tensor, named after Wilhelm Killing, is a symmetric tensor, known in the theory of general relativity, that satisfies
where the parentheses on the indices refer to the symmetric part.
This is a generalization of a Killing vector. While Killing vectors are associated with continuous symmetries (more precisely, differentiable), and hence very common, the concept of Killing tensor arises much less frequently. The Kerr solution is the most famous example of a manifold possessing a Killing tensor.