Geodesic
Lie Point Symmetries, Hamiltonian Equations and Conservation Laws of the Geodesics on a Schwarzschild Black Hole
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 453

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Classification of Schwarzschild geodesics via group analysis of Lie point symmetries is considered. Lie's symmetry method of differential equations (DEs) is applied to the system of Schwarzschild geodesics to classify geodesic curves. In this method Lie algebra of symmetries will be studied and some useful results in physics such as Hamiltonian equations and conservation laws are obtained.
Classification : 58J70 76M60
Keywords: Schwarzschild metric, symmetry, Lie algebra, conservation laws, Hamiltonian equations 
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     author = {S. Reza Hejazi},
     title = {Lie {Point} {Symmetries,} {Hamiltonian} {Equations} and {Conservation} {Laws} of the {Geodesics} on a {Schwarzschild} {Black} {Hole}},
     journal = {Kragujevac Journal of Mathematics},
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     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a10/}
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S. Reza Hejazi. Lie Point Symmetries, Hamiltonian Equations and Conservation Laws of the Geodesics on a Schwarzschild Black Hole. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 3, p. 453 . http://geodesic.mathdoc.fr/item/KJM_2018_42_3_a10/