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On the invariance properties of Vaidya-Bonner geodesics via symmetry operators | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 43، دوره 13، شماره 1، خرداد 2022، صفحه 563-571 اصل مقاله (369.81 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.21159.2238 | ||
| نویسندگان | ||
| Davood Farrokhi1؛ Rohollah Bakhshandeh Chamazkoti* 2؛ Mehdi Nadjafikhah3 | ||
| 1Department of Mathematics, Karaj Branch, Islamic Azad University, karaj, Iran. | ||
| 2Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Babol, Iran | ||
| 3School of Mathematics, Iran University of Science and Technology Narmak, Tehran, 16846-13114, Iran | ||
| تاریخ دریافت: 30 مرداد 1399، تاریخ بازنگری: 23 مهر 1399، تاریخ پذیرش: 17 آبان 1399 | ||
| چکیده | ||
| In the present paper, we try to investigate the Noether symmetries and Lie point symmetries of the Vaidya-Bonner geodesics. Classification of one--dimensional subalgebras of Lie point symmetries are considered. In fact, the collection of pairwise non-conjugate one--dimensional subalgebras that is called the optimal system of subalgebras is determined. Moreover, as illustrative examples, the symmetry analysis is implemented on two special cases of the system. | ||
| کلیدواژهها | ||
| determining equations؛ Lie point symmetry؛ Noether's theorem؛ optimal system؛ prolongation | ||
| مراجع | ||
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[1] R. Bakhshandeh-Chamazkoti, Symmetry analysis of the charged squashed Kaluza-Klein black hole metric, Math. Meth. Appl. Sci. 39 (2016) 3163–3172. [2] R. Bakhshandeh-Chamazkoti, Geometry of the curved traversable wormholes of (3 + 1)-dimensional spacetime metric, Int. J. Geom. Meth. Mod. Phys. 14(4) (2017) 1750048. [3] H. Bokhari, A.H. Kara, A.R. Kashif and F. Zaman, Noether symmetries versus killing vectors and isometries of spacetimes, Int. J. Theor. Phys. 45 (2006) 1063. [4] H. Bokhari and A.H. Kara, Noether versus Killing symmetry of conformally flat Friedmann metric, Gen. Relativ. Grav. 39 (2007) 2053–2059. [5] I.H. Dwivedit and P.S. Joshi, On the nature of Naked singularities in Vaidya spacetimes, Class. Quant. Grav. 6 (1989) 1599. [6] N. H. Ibragimov, Elementary Lie group analysis and ordinary differential equations, Chichester: Wiely, 1999. [7] D.N. Khan Marwat, A.H. Kara and F.M. Mahomed, Symmetries, conservation laws and multipliers via partial Lagrangians and Noether’s theorem for classically non-variational problems, Int. J. Theor. Phys. 46 (2007) 3022– 3029. [8] Z.-F. Niu and W.-B. Liu, Hawking radiation and thermodynamics of a Vaidya-Bonner black hole, Res. Astron. Astrop. 10(1) (2010) 33–38. [9] R. Narain and A.H. Kara, The Noether conservation laws of sme Vaidiya metrics, Int. J. Theor. Phys. 49 (2010) 260–269. [10] R. Narain and A.H. Kara, Invariance analysis and conservation laws of the wave equation on Vaidya manifolds, Pramana J. Phys. 77(3) (2011) 555–570. [11] E. Noether Invariante variations probleme, Nachr. Akad. Wiss. Gott. Math. Phys. Kl. 2 (1918) 235–57 (English translation in Transp. Theory Stat. Phys. 1(3) (1971) 186–207). [12] P.J. Olver, Applications of Lie groups to differential equations, New York: Springer, 1986. [13] L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982. [14] M. Tsamparlis and A. Paliathanasis, Lie and Noether symmetries of geodesic equations and collineations, Gen. Relativ. Gravit. 42 (2010) 2957–2980. [15] M. Tsamparlis and A. Paliathanasis, Lie symmetries of geodesic equations and projective collineations, Nonlinear Dyn. 6(2) (2010) 203–214. | ||
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