Journal
JOURNAL OF GEOMETRY AND PHYSICS
Volume 61, Issue 3, Pages 658-662Publisher
ELSEVIER
DOI: 10.1016/j.geomphys.2010.11.015
Keywords
Noether symmetries; Conserved quantities; Conformally flat spacetimes
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In an earlier paper (Feroze, 2010[21]), the existence of new conserved quantities (Noether invariants) for spaces of different curvatures was discussed. There, it was conjectured that the number of new conserved quantities for spaces with an m-dimensional section of zero curvature is m. Here, along with the proof of this conjecture, the form of the new conserved quantities is also presented. For the illustration of the theorem, an example of conformally flat spacetime is constructed which also demonstrates that the conformal Killing vectors (CKVs), in general, are not symmetries of the Lagrangian for the geodesic equation. (C) 2010 Elsevier B.V. All rights reserved.
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