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Noether versus Killing symmetry of conformally flat Friedmann metric. (English) Zbl 1136.83010
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.

83C15 Exact solutions to problems in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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[1] Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation Benjamin, New York (1973)
[2] Petrov A.Z. (1969). Einstein Spaces. Pergamon, Oxford · Zbl 0174.28305
[3] Stephani H., Kramer D., MacCallum M.A.H., Hoenselaers C. (2003). Exact solutions of Einstein Field Equations. Cambridge University Press, Cambridge · Zbl 1057.83004
[4] Katzin, G.H., Levine, J.: Coloq. Math. 26, (21) (1972)
[5] Hall, G.S.: Symmetries and curvature structure in general relativity. World Scientific, (2004) · Zbl 1054.83001
[6] Bokhari A.H., Kashif A.R. (1996). J. Math. Phys. 37(7): 3496 · Zbl 0865.53072 · doi:10.1063/1.531577
[7] Giachetta, G., Sardanashvily, G.: Stree-energy-momentum tensors in Lagrangian field theory, arXiv:gr-qc/9510061
[8] Camci U., Barnes A. (2002). Class. Quantum Grav. 19: 393 · Zbl 0996.83064 · doi:10.1088/0264-9381/19/2/312
[9] Nunez L.A., Percoco U., Villalba V.M. (1990). J. Math. Phys. 31: 137 · Zbl 0717.53014 · doi:10.1063/1.528872
[10] Bokhari A.H. (1992). Int. J. Th. Phys. 31: 2091 · Zbl 0770.53012 · doi:10.1007/BF00679968
[11] Amer M.J., Bokhari A.H., Qadir A. (1994). J. Math. Phys. 35(6): 3005 · Zbl 0817.53047 · doi:10.1063/1.530499
[12] Marteen, R., Maharaj, S.D.: Class. Quantum Grav., 3, 1005 (1986)
[13] Fatibene L., Ferraris M., Francaviglia M., McLenaghan R.G. (2002). J. Math. Phys. 43(6): 3147 · Zbl 1059.70021 · doi:10.1063/1.1469668
[14] Mangiarotti L., Sardanashvily G. (2000). Connections in classical and quantum field theory. World Scientific, Singapore · Zbl 1053.53022
[15] Bokhari A.H., Kara A.H., Kashif A.R., Zaman F.D. (2006). Int. J. Th. Phys. 45(6): 1063 · Zbl 1125.83305 · doi:10.1007/s10773-006-9096-1
[16] Wolf, T.: Crack, LiePDE, ApplySym and ConLaw, section 4.3.5 and computer program on CD-ROM. In: Grabmeier, J., Kaltofen, E., Weispfenning, V. (eds.) Computer Algebra Handbook, vol. 465. Springer, Heidelberg (2002)
[17] Wolf T. (2004). Applications of CRACK in the classification of integrable systems. CRM Proc. Lect. Notes 37: 283 · Zbl 1073.37081
[18] Bokhari, A.H.: Conformal extension of Pseudo-Newtonian Formalis, PhD Thesis, Quaid-i-Azam University (1985)
[19] Kara A.H., Mahomed F.M., Vawda F.E. (1994). Lie groups and their applications 2: 27 · Zbl 0920.35010
[20] Kara A.H., Khalique C.M. (2005). J. Phys. A 38: 4629 · Zbl 1069.37047 · doi:10.1088/0305-4470/38/21/008
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