The Noether Conservation Laws of Some Vaidiya Metrics |
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Authors: | R Narain and A H Kara |
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Institution: | (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 Applications, University of the Witwatersrand, Wits 2050, Johannesburg, South Africa;(3) Department of Mathematics, National University of Science and Technology, Rawalphindi, Pakistan; |
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Abstract: | In this paper, we show that a large amount information can be extracted from a knowledge of the vector fields that leave the
action integral invariant, viz., Noether symmetries. In addition to a larger class of conservation laws than those given by
the isometries or Killing vectors, we may conclude what the isometries are and that these form a Lie subalgebra of the Noether
symmetry algebra. We perform our analysis on versions of the Vaidiya metric yielding some previously unknown information regarding
the corresponding manifold. Lastly, with particular reference to this metric, we show that the only variations on m(u) that occur are m=0, m=constant, m=u and m=m(u). |
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