# Killing tensor: Difference between revisions

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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 | A '''Killing tensor''', named after [[Wilhelm Killing]], is a symmetric [[tensor]], known in the theory of [[general relativity]], <math>K</math> that satisfies | ||

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where the parentheses on the indices refer to the [[symmetric tensor|symmetric part]]. | 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. | This is a generalization of a [[Killing vector]]. While Killing vectors are associated with [[Continuous symmetry|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== | ==See also== |

## Latest revision as of 21:18, 18 August 2014

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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.