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Zbl 1136.83010
Bokhari, Ashfaque H.; Kara, A.H.
Noether versus Killing symmetry of conformally flat Friedmann metric. (English)
[J] Gen. Relativ. Gravitation 39, No. 12, 2053-2059 (2007). ISSN 0001-7701; ISSN 1572-9532/e

Summary: In a recent study Noether symmetries of some static spacetime metrics in comparison with Killing vectors of corresponding spacetimes were studied. It was shown that Noether symmetries provide additional conservation laws that are not given by Killing vectors. In an attempt to understand how Noether symmetries compare with conformal Killing vectors, we find the Noether symmetries of the flat Friedmann cosmological model. We show that the conformally transformed flat Friedman model admits additional conservation laws not given by the Killing or conformal Killing vectors. Inter alia, these additional conserved quantities provide a mechanism to twice reduce the geodesic equations via the associated Noether symmetries.

MSC 2000:: *83C15 Closed form solutions of equations in general relativity
83C05 Einstein's equations

Keywords: Noether symmetry; Killing vector; Conformal Killing vector

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