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Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric

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Abstract

Approximate symmetries have been defined in the context of differential equations and systems of differential equations. They give approximately, conserved quantities for Lagrangian systems. In this paper, the exact and the approximate symmetries of the system of geodesic equations for the Schwarzschild metric, and in particular for the radial equation of motion, are studied. It is noted that there is an ambiguity in the formulation of approximate symmetries that needs to be clarified by consideration of the Lagrangian for the system of equations. The significance of approximate symmetries in this context is discussed.

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Authors and Affiliations

  1. Centre for Differential Equations, Continuum Mechanics and Applications, School of Mathematics, University of Witwatersrand, Wits 2050, Johannesberg, South Africa

    A. H. Kara

  2. Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of Witwatersrand, Wits 2050, Johannesberg, South Africa

    F. M. Mahomed

  3. Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of the College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan

    Asghar Qadir

  4. Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Asghar Qadir

Authors
  1. A. H. Kara
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  2. F. M. Mahomed
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  3. Asghar Qadir
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Correspondence to F. M. Mahomed.

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Kara, A.H., Mahomed, F.M. & Qadir, A. Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric. Nonlinear Dyn 51, 183–188 (2008). https://doi.org/10.1007/s11071-007-9201-x

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  • DOI: https://doi.org/10.1007/s11071-007-9201-x

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