General Relativity and Gravitation

, Volume 39, Issue 12, pp 2053–2059

Noether versus Killing symmetry of conformally flat Friedmann metric

Research Article

Abstract

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.

Keywords

Noether symmetry Killing vector Conformal Killing vector 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  2. 2.School of Mathematics and Centre for Differential Equations, Continuum Mechanics and ApplicationsUniversity of the WitwatersrandJohannesburgSouth Africa

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