International Journal of Theoretical Physics, Vol. 45, No. 6, June 2006 ( C  2006) DOI: 10.1007/s10773-006-9096-1 Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes A. H. Bokhari, 1 A. H. Kara, 2 A. R. Kashif, 3 and F. D. Zaman 1 Received August 2005; accepted January 2006 Published Online: May 10, 2006 Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the ex- amples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra. KEY WORDS: Noether symmetries; isometries of spacetimes; Lie algebras. PACS: 04.25.g, 02.20.Sv, 11.30.j 1. INTRODUCTION The Einstein field equations which govern the general theory of relativity (GR) are described in terms of the 4-Lorentzian metric g ab and are highly non-linear equations. It has therefore been one of the fundamental problems in GR to find and understand solutions of the Einstein field equations through the symmetries they possess, see Meisner et al. (1973). These symmetries are given by Killing vectors (KVs): a KV is the one along which the Lie derivative of the metric is zero. Since these symmetries are pivotal to understand the physics of the gravitational fields, they have been throughly investigated and by now a large body of literature is available on them (Petrov, 1969). As fas as the KVs are concerned, they form a finite dimensional Lie group for the spacetime metric being non-degenerate. On the one hand the metric conservation laws are pivotal to study the symmetry groups admitted by them, there are other tensors of more physical interest whose 1 Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. 2 School of Mathematics and Centre for Differential Equations, Continuum Mechanics and Applica- tions, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa. 3 College of Electrical and Mechanical Engineering National University of Scieces and Technology Peshawar Road, Rawalpindi, Pakistan. 1063 0020-7748/06/0600-1063/0 C  2006 Springer Science+Business Media, Inc.